Parsons tweeted Sunday after he said he heard from Rockets general manager Daryl Morey and owner Leslie Alexander about the team's decision.
''Nothing but utmost respect for them, the fans and the city of Houston. THANK YOU for your support!,'' Parsons wrote before following that with another farewell tweet.
''Houston will always have a special place in my heart and I will never forget the memories. My teammates, I love you, thank you,'' his second entry read.
The 6-foot-9 small forward signed the offer sheet early Thursday, only minutes after the NBA's moratorium on signing free agents ended. Houston had until Sunday to match.
Mark Cuban welcomed Parsons to Dallas in a message Sunday afternoon on a Cyber Dust account controlled by the Mavericks owner and the team.
Dallas also struck a deal with free agent veteran swingman Richard Jefferson on a one-year minimum deal.
Parsons will be in the Dallas frontcourt with Dirk Nowitzki and recently reacquired Tyson Chandler after playing his first three NBA seasons with the Rockets.
The 25-year-old Parsons has averaged 14.1 points, 5.2 rebounds and 4.1 assists while starting 207 of his 213 games in the NBA. He was a second-round pick out of Florida in the 2011 draft.