"Norwegian" is two languages - Bokmål ("book language") and Nynorsk ("new Norwegian").
Both are constructed, and not just bits and pieces, though they were constructed from "natural" elements.
Bokmål came into being through a series of drastic reforms of a combination of Danish (which was the administrative language until the dissolution of the union with Denmark in 1814) and urban Norwegian dialects, which were heavily influenced by Danish.
The reforms were aimed at removing a lot of the Danish influence, and continued well into the 20th century (well, in a sense they are still continuing, though making Bokmål less Danish is no longer an explicit goal). Many of the changes took decades to take root as most adults didn't really change but school children were taught and graded on the new forms.
E.g. the change from Danish word-order in numbers ("fireogtyve" - 24 - "fire-og-tyve = four and twenty") to uniformity with less formal spoken Norwegian dialects ("tjuefire" - "twentyfour") is one that was still for all intents ongoing at least well into the 80's (you'll still find older people using the old forms today) despite being introduced by a language reform in 1951. My parents learned the new form in primary school in the late 50's yet still regularly reverted to the old form around me while I was growing up in 70's and 80's, and as a result I used to switch back and forth between the two at least into my 20s (in the 90's)
(Incidentally these reforms also means that for Norwegians learning German, spending some time reading old Norwegian books is highly helpful to get used to German word order and even recognizing vocabulary, as the reforms that moved Bokmål away from Danish also moved it further away from German)
Nynorsk, meanwhile, was explicitly created as a form of unification of a number of very different rural Norwegian dialects. This included synthesising a grammar, creating a bunch of new words that tried to find forms that were "close enough" to the widest possible range of dialects, and combining a lot of other elements from different dialects.
Bokmål is used as the written language of the vast majority, despite most spoken dialects probably in many ways being closer to Nynorsk (though more so in some parts of the country than others - Norwegian dialects are extremely varied). In some parts Bokmål - particularly spoken Bokmål - has a tendency to be seen as more refined, as a remnant of their historical origins. An unofficial dialect - Riksmål - is basically Bokmål sans a number of the reforms, and remains much closer to Danish. It sees very little use, though well into the 80's one of the largest conservative newspapers stuck to a lot of the Riksmål forms.
Bokmål and Nynorsk are mutually intelligible, and successive language reforms over more than a century have aimed to bring them closer (largely by creating optional forms of many words that are consider valid in both languages), but having to learn both is a frequent cause of discontent at Norwegian schools (it annoyed me immensely, because unlike most Norwegians I speak very close to pure Bokmål, and a relatively conservative form of it, as a legacy of my dads upbringing and reading a lot of old books growing up, which made Nynorsk harder)
While the reforms do take into account natural language shifts to some extent, large parts of the current modern structure of both languages was effectively created by academics.