Beasley, 32, started all four games for the USA at the 2014 World Cup, and in the process became the first American to play in four World Cups.
The veteran joins Houston after spending three seasons with Puebla F.C. in Liga MX. His contract was expired, making him a free agent.
“I am excited and ready to start this new chapter in my career,” Beasley said in a club release. “I have heard great things from Brad (Davis) and Rico (Clark) about Houston, the team and the fans, and I’m excited to get to know them. I feel fit and ready to go and hope Dom (Kinnear) will see my work ethic and desire to play at a high level.”
Beasley’s club career has also included time with Hannover 96 (German Bundesliga), Rangers (Scottish Premier League), Manchester City (Barclays Premier League), PSV Eindhoven (Dutch Eredivisie) and the Chicago Fire.
Earlier Wednesday, Dynamo traded midfielder Warren Creavalle to Toronto FC in exchange for the No. 1 ranking in the MLS allocation order and allocation money.