Making that ">=" would make that entire "if" check redundant, since we already know it's at least 365 (because of the "while" condition)

I think the "while" condition should actually be

    while ((days > 365 && !IsLeapYear(year)) || (days > 366 && IsLeapYear(year)))

(or perhaps some simplification that I'm too lazy to figure out right now)

And then the inner "if" condition can be eliminated. Thus the final code could be:

    while ((days > 365 && !IsLeapYear(year)) || (days > 366 && IsLeapYear(year)))
    {
        if (IsLeapYear(year))
            days -= 366;
        else
            days -= 365;
        year += 1;
    }

This seems logical and easier to understand than the original too.

Edit: if you want to get ternary-operator fancy:

    while (days > (IsLeapYear(year) ? 366 : 365))
    {
        days -= IsLeapYear(year) ? 366 : 365;
        year += 1;
    }