In Canada, you get an Open Work Permit as soon as you finish your degree. The length of the work permit depends on the type and length of the program. Once you get a proper job (full-time, related to your degree), you file for Permanent Residency, which if all checks out, takes around 6-8 months to process.

Source: did my undergrad in US, spent 5 miserable years on H1B tied to a single employer who kept delaying my PR application, because of which I couldn't travel freely internationally. Moved to Canada, finished my Masters, got my PR in 6 months. Now I can travel whereever I want. Thanks, Trudeau!

>Can an american get a work visa and get permanent residency in EU countries with ease

Nothing is easy, especially when it comes to moving countries.

I can offer insight on the Netherlands specifically. Other EU countries might have similar systems in place, though each is different.

There are generally three options for an American to move to the Netherlands for work:

1) get a highly-skilled job outright with a Dutch company that fulfills certain criteria in a position which cannot be filled locally. Not all companies are eligible to hire highly-skilled migrants from abroad (they have to apply to do so, and there are considerable costs involved). There are some nice tax perks to this (see 30% ruling).

2) start your own business with relatively small investment capital (<5000eur) and gain residence through the Dutch-American Friendship Treaty (https://en.wikipedia.org/wiki/DAFT)

3) get a Master's degree from a Dutch university, after which you'll have full access to the Dutch job market for one year, then you'll receive a highly-skilled migrant work visa

The above provide a path to a renewable residence permit for highly-skilled migrants. Typically you'll start working with a temporary 1-yr contract which, assuming things go well, will be extended for another year. After 2 years of temporary contracts and if the company still wants to keep you they'll give you an indefinite contract. After this, you'll next receive a highly-skilled migrant visa valid for 5 years.

An American is eligible for permanent residence after having lived uninteruppted in the Netherlands for 5 years and after passing an integration test. The integration test requires that you speak Dutch, though honestly this is not so difficult (it's at an A1 level and the tests are fairly basic; they also test your ability to function in the Dutch job market and society which is a bit silly to ask of a highly-skilled migrant who's already successfully lived there for 5 years).

I'm sort of in the process of gaining permanent residence. I have the time, the degree, the job, and most of the Dutch; it's only a matter of passing the test and submitting the paperwork. But since I have a 5-yr permit and permanent job contract already I'm not in a major rush.

edit: I feel like it's important to point out that the highly-skilled migrant permit is obtained for you on behalf of your employer, however it is not tied to that employer. You're free to find other work elsewhere without any retribution.

I can speak for NZ. I originally got a Holiday Work visa (if you're under 30, America has several agreements. You can live and work in Australia, New Zealand, Ireland if you just graduated and a few other countries. I highly recommend them).

My holiday work visa ran out and I switched to an Essential Skills visa. I wish I had ticked the other box and gotten "Work to Residence." It cost more but you get a residence without travel restrictions after a few years. You can also apply for a full resident (a few thousand dollars) visa and you become a resident, but with travel restrictions. If you leave for more than six months, you lose it. If you stay past a certain point (I think it was 2 years or something like that), you can apply for a permanent resident without travel restrictions.

The US doesn't have the concept of "Resident without travel restrictions." If a customs agent asks you questions and thinks you don't actually live in the US (e.g. you only visit once a year), you can potentially lose that green card. It's arbitrary though, because the US is only of the only countries that doesn't do a customs check on exit (it's impossible to determine if someone overstays in America, unlike every other developed country in the world).

For most countries, to immigrate you must be on their essential skills list. I've considered getting another Australian visa (I lived there too; holiday work visa only), and the process involves putting in a letter of intent. If you're selected, you can apply. The fees are steep (usually a few thousand dollars), but if you're selected, you get residence and a window which you must arrive by. After a few years of holding a job or being able to support yourself in your field, you can apply for permanent residence.

Immigration without an essential skill is extremely difficult, for all countries. This is a stark contrast to immigration only a few decades ago, when countries like the US and Australia were in desperate need of all types of workers.

For France: It takes about one month to get a long term work visa for if you have a job (the name is a trick, it's just one year). Then you can upgrade from inside the country up to naturalization (it's a long journey, something like 10 years from first entry to passeport), you are not tied to your first employer after the visa is issued. There are some really disagreeable moments, when you have to go to the Prefecture, but I think the entire procedure is free*

* actually you might have to pay to get some translations certified, or if you want a lawyer.

I even know 2 Americans citizen who have a long term self employed permit.

One detail: you can travel all over the Schengen Zone for tourism, but you still can work only in one country.

It depends on the country. It ranges from much easier (compared to the other way around) to quite hard. There may be quotas but no lottery involved though.

A lot of EU countries have programs that do not tie the work visa with a specific job, at least for engineers. On the top of my head, Portugal,Sweden,Germany and Belgium do and France with implement some form of "tech visa" like that. Canada does too AFAIK. I think it's fair. "H1-B" should be paid as much as their local equivalent and shouldn't fear being fired.

I don't know the process, but 2 of my (American) coworkers recently left my company (in the US) to work for companies in Europe.

Didn't seem at all hard to get to work there. Don't know about permanent residency, though.