The team signed the left-handed pitcher on Wednesday to a minor league contract with an invitation to major league spring training.
Once known as the "D-Train," Willis won the National League rookie of the year award in 2003 while with the Marlins. He hopes to return to the majors for the first time since 2011, when he was 1-6 in 13 starts with the Cincinnati Reds.
Willis, who will be 34 in January, has bounced around since then on minor league deals. Brewers General Manager Doug Melvin said that a couple of scouts saw Willis and reported that it looked as if he had a shortened delivery.
The Rangers were already working on the Corporan deal when they got pitcher Yovani Gallardo in a trade with Milwaukee on Monday.
Houston designated Corporan for assignment Tuesday, setting up the trade for 19-year-old minor league pitcher Akeem Bostick. The Rangers selected the right-hander in the second round of the 2013 amateur draft.
Corporan, the Astros' backup catcher the last four seasons, is expected to have that same role in Texas behind Robinson Chirinos.
The Cincinnati Reds and right-hander Jason Marquis have reached agreement on a minor league contract that includes an invitation to spring training.
The Giants said they plan to retain Scutaro and continue working with him through his rehabilitation following back surgery that could end his career. It will be four-to-six months before doctors determine whether Scutaro can play baseball again.