Barmes has played mostly second base with the Rockies in recent years but was the starting shortstop for a month this year while Troy Tulowitzki was injured.
Barmes talked with Astros manager Ed Wade and manager Brad Mills after the deal and was told he'd be mostly playing shortstop.
"I feel like I'm an everyday shortstop," Barmes said. "I've always believed that and playing with the Rockies these last couple of years, I've looked at myself as a shortstop playing second base. I'm very excited to get the opportunity to play on that side of the field again."
The 31-year-old Barmes hit .235 with 21 doubles, eight homers and 50 RBIs in 387 at-bats this year. He hit .245 with 23 homers and 76 RBIs in 2009, when he was Colorado's starting second baseman.
"He's a plus defensive player at two positions, has gap and some home run power and has great makeup," Wade said. "It's tough to give up a power arm like Felipe's, but Clint fits a need that we had to address."
Barmes has played in the majors in parts of eight seasons and has a .254 career average with 61 home runs and 285 RBIs.
He started 69 games at second base and 39 games at shortstop last season. He hit .284 with three home runs and 12 RBIs in the 32 games he started in place of Tulowitzki. Though he prefers shortstop, he remains open to playing other places for the Astros.
"I'm excited to get the opportunity to play, whatever position that comes up," he said. "I know I can play multiple positions if that's what they need."
The 27-year-old Paulino was 1-9 with a 5.11 ERA in 14 starts and five relief appearances this year, which would have been the highest ERA among NL pitchers had he thrown enough innings to qualify. He is 6-21 with a 5.83 ERA in parts of three seasons.
Paulino joined the Astros as an undrafted free agent in 2001.