Red Bulls sporting director Andy Roxburgh announced the deal Thursday, saying Martinez is a young player with potential and the allocation money will provide financial flexibility for the team.
The 22-year-old Martinez started six of 18 games last season and had one goal. He has 16 caps for Costa Rica and has scored two goals.
Le Toux's contract with New York ended after last season. He was acquired from Vancouver in July for Dane Richards and allocation money. He had a goal and an assist in 14 games.