Adames is hitting .197 with five homers and 15 RBIs in 41 games this year but had an .813 OPS last season while helping Tampa Bay reach the World Series. The 28-year-old Richards has a 4.50 ERA and one save in six relief appearances.
"We're acquiring a shortstop who has proven he's one of the best defensive shortstops in baseball," Brewers president of baseball operations David Stearns said.
The trade surprised Adames, who already had arrived at TD Ballpark for the Rays' game with the Toronto Blue Jays in Dunedin, Florida, when he learned about the move. Adames said he'd "been crying the whole afternoon.''
"To get that news out of nowhere, it was tough,'' Adames said. "It's business. You've got to see every side of the situation and every view and just take the positive, and just bring the joy with everything we've done here. Just continue to have those memories and take it with me."
The Rays plan to call up Taylor Walls and give him much of the playing time at shortstop, though Joey Wendle will play there on occasion. Tampa Bay also has top prospect Wander Franco and Vidal Brujan at Triple-A Durham.
"You're talking about as good a defensive shortstop as you're going to find,'' Rays general manager Erik Neander said. "You're talking about a switch-hitter that can put ball in the play, do a lot of things to help you win tight games.''
Adames said he figured he might get traded eventually because the Rays had Walls and Franco in the organization. He just didn't think a deal would happen this soon.
"That's what I was telling the guys,'' Adames said. "I said, 'It was so surprising because it's too early.' I was not even thinking this year, maybe next year. You kind of knew that's how they work, that's how the organization works. But to get this news so early, it was tough."
Neander said Feyereisen will fill an immediate role in Tampa Bay's bullpen while Rasmussen will get sent to Durham.
The 28-year-old Feyereisen is 0-2 with a 3.26 ERA in 21 games this season, though he has allowed six runs over 1 1/3 innings in his past two appearances. Rasmussen, 25, is 0-1 with a 4.24 ERA and one save in 15 games.
"Their arms we believe have end-of-game potential,'' Neander said.
The acquisition of Adames gives the Brewers some help at shortstop, which had been a growing concern. The Brewers began a weekend series at Cincinnati on Friday having lost 12 of their past 16 games to fall below .500.
Milwaukee handed its starting shortstop job to 23-year-old Luis Urias this year and showed its faith in him last month by trading Orlando Arcia to the Atlanta Braves. Arcia had been the Brewers' starting shortstop from 2017 to '20.
Urias is hitting .205 and has nine errors in 38 games. He had consecutive two-error games Sunday against Atlanta and Tuesday at Kansas City.
Brewers officials said they'd been interested in Adames long before Urias' recent fielding struggles.
"We've been talking with Tampa about Willy for months, really,'' Stearns said. "And it just got going again over the past week and we were able to get a deal done this morning.''
Urias now will fill more of a utility role. Most of his starts figure to come at third base, though he also can help out at second and shortstop.
"Young players are asked to continually prove themselves,'' Brewers manager Craig Counsell said. "Luis is going to be asked to prove himself again, just like every player is. Luis is up for the challenge. I believe that. And I believe he's going to be a productive member of the team.''
Adames gives the Brewers a more polished shortstop who should team up with two-time Gold Glove second baseman Kolten Wong to give Milwaukee quality defense up the middle.
Adames has a $590,000 salary in the major leagues, is eligible for arbitration next winter and can become a free agent after the 2024 season.,
Richards has a $580,900 salary in the major leagues and also is eligible for arbitration after this season. Feyereisen is a rookie, and Rasmussen began the season with less than one year of major league service.