The clubs exchanged allocation ranking positions in the deal, moving Houston to the top of the list while Toronto dropped to No. 14. MLS uses the allocation ladder to regulate players returning to the league.
Toronto also sent allocation money to Houston, which would help in paying for Beasley.
Creavalle adds depth across a variety of positions for Toronto.
The 23-year-old Brooklyn native has three goals in 54 regular-season appearances for Houston. He was taken in the second round of the 2012 MLS SuperDraft out of the University of Central Florida and has played across the midfield and defence in MLS.
"Warren is a player that we have been watching closely for some time now and we feel his versatility will be a welcomed addition to our club," Toronto GM Tim Bezbatchenko said in a statement. "Houston expressed interest in switching allocation positions so combined with our interest in Warren this move was a win-win for both clubs."
Beasley, 32, is a former Chicago Fire player who has spent 10 years abroad, most recently with Mexico's Puebla. He has also played for PSV Eindhoven, Manchester City, Glasgow Rangers and Hannover.
"I am excited and ready to start this new chapter in my career," Beasley said in a statement. "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 (coach Dominic Kinnear) will see my work ethic and desire to play at a high level."
Beasley, who can also play on the wing, has won 120 caps for the U.S. and played in four World Cups.
He skipped college to enter MLS as a Project-40 player in 1999 when he was 16 and was assigned to the Los Angeles Galaxy. He was traded to Chicago before ever playing for the Galaxy.
Houston (5-11-4) has struggled all season, hampered by injuries and the World Cup absences of Garcia and U.S. midfielder Davis. The Dynamo are winless in eight matches (0-6-2) and have given up a league-worst 40 goals.
"DaMarcus has had a great career, as we saw at the World Cup," Kinnear said. "To bring in a player of his quality is a big plus for the team."
Boniek Garcia is the Dynamo's other current senior designated player. Fellow Honduran midfielder Alexander Lopez is considered a young DP.