Is it legal for my employer to pay me only after a job is complete even though it may take months?

It depends on whether you are in fact an indepenent contractor (properly paid by a 1099) or an employee. An independent contractor, like a vendor or a professional, such as a lawyer, accountant, freelance graphic artist, etc., can be paid legally when a job is done. Independent contractors are not employees.
However, an employee must be paid every two weeks or twice a month.
Many employers mischaracterize employees as independent contractors--that is, they call employees (and pay them as) independent contractors when they are not. It doesn't matter what the employer wants to call an employee or whether they give them a 1099 or not; the issue is, does the worker meet the test or criteria to be an independent contractor or not. If they don't qualify as an independent contractor, they must be paid as an employee--every two weeks, having income tax withholding taken out, have the employer pay the employer potions of Medicare, social security, etc.
You can find the full criteria for when someone is an independent contractor on the U.S. Dept. of Labor website. But in brief, an independent contractor IS "independent" to a considerable degree: sets own hours; decides where to work for the most part; decides how to do the job; typically works for more than one person or client at a time; markets or advertises own services; provides own tools and equipment; etc. If this doesn't sound like you--if you work for one employer, during hours the employer chooses, at the employer's site, etc.--then you are most likely an employee and need to be paid as an employee.