Myers had 19 saves and a 3.52 ERA for the Astros this season and will try to bolster an inexperienced Chicago bullpen. Addison Reed, Chicago's 23-year-old closer, has 15 saves but a 4.24 ERA. Rookie Nate Jones has a 3.57 ERA in 35 appearances.
White Sox general manager Kenny Williams said Myers would not be Chicago's closer.
"In no way, for [manager Robin Ventura] or myself or in any way, is this a lack of confidence in Addison Reed," Williams said.
The White Sox entered Saturday's game at Detroit with a half-game lead on the Tigers atop the AL Central.
"It's time to make a push," Williams said. "He's an intense competitor. He makes our bullpen better."
The Astros are in last place in the NL Central and had little need to keep Myers, a 31-year-old righthander. Houston receives righthander Matt Heidenreich and lefthander Blair Walters. Chicago also receives cash considerations from Houston in the deal.
Bryce Harper left the Nationals' 4-0 first-game loss against the Braves because of a bruised left ankle.
X-rays were negative, according to manager Davey Johnson, who was uncertain if the 19-year-old would play in the finale of Saturday's day-night doubleheader. He did return as a pinch hitter in the nightcap.
Harper fouled a bunt off his ankle in the bottom of the first inning of the opener. Limping and doubled over in pain for several moments, he completed the at-bat by striking out.
The first time All-Star returned to centerfield in the second inning, but Roger Bernadina replaced him on defense for the top of the third with the Nationals trailing 1-0.