The deal comes just one day after it was announced that Bucks guard Khris Middleton, who averaged a career-high 18.2 points per game last season, is expected to miss six months after suffering a torn left hamstring during a preseason workout. He will undergo surgery next week.
The 6-foot-9 Beasley was signed by the Rockets late last season after spending time with the Shandong Golden Stars of the Chinese Basketball League. In 20 games with Houston, Beasley averaged 12.8 points over 18.2 minutes per game.
"We're excited to add a player with Michael's skill set to our team," Bucks general manager John Hammond said in a statement. "He's someone that we've kept our eye on the last few seasons and we're looking forward to watching him compete throughout training camp and the season."
The acquisition of the 6-3 Ennis provides depth for the Rockets at point guard. A 2014 first-round pick of the Suns, Ennis was dealt to the Bucks last season as part of a three-team trade.
He played in 46 games with seven starts last season, averaging 4.5 points and 2.1 assists per game.
The Rockets start training camp Saturday, while the Bucks begin next week.