If I signed a non-compete with my former employer but I quit and went to another company, can they legally make me quit my new job?

No, your old employer cannot force you to quit. Base at least on breach of contract ( i.e., the non-compete clause ), the old employer can file a lawsuit against you and maybe even the new employer. You potentially could have to pay monetary damages. However, the terms of the non-compete clause must be reasonable in terms of years and geographic distance. There is Law that requires that, at the onset of your employment, you must have received compensation for the non-compete clause. You need a lawyer to reveiw the precise language of the non-compete clause and whether you were properly compensated ( separately ) for that clause.Good luck.