Greinke is scheduled to make his Angels debut Sunday when they close their series against the Tampa Bay Rays.
Los Angeles (55-46) acquired Greinke, arguably the most coveted arm on the trade market, from Milwaukee on Friday in exchange for rookie shortstop Jean Segura and Double-A right-handers Ariel Pena and Johnny Hellweg.
Greinke joins a rotation led by Weaver, who is 13-1 with an AL-leading 2.26 ERA, and Wilson, who was outdueled by Matt Moore in a 3-0 loss to the Rays on Saturday but is still among the top pitchers in the AL with a 2.88 ERA.
"He wants to win, and he's proven that over the course of his career," Weaver said of Greinke. "He brings a winning mentality. He's got electric stuff and he's fun to watch, so I'm looking forward to what he brings to the table. I think he can help out, no doubt about it."
The 2009 AL Cy Young Award winner with Kansas City, Greinke was 9-3 with a 3.44 ERA in 21 starts with the Brewers. In his last start, he gave up one run and three hits in seven innings of a 7-6 win against Philadelphia on Tuesday, but didn't factor in the decision.
The right-hander will see if his success at home extends to a third city. He has won 19 straight decisions at home dating back to 2010 with Kansas City.
Greinke is 2-4 with a 3.32 ERA versus the Rays, posting a 1.64 ERA in his last three meetings. He'll have Chris Iannetta behind the plate after the Angels catcher was activated off the disabled list Saturday following wrist surgery in May.
The Angels hope the addition of Greinke can help them close the gap in the AL West. Saturday's loss dropped them into third place behind Texas and red-hot Oakland. They are four games behind the first-place Rangers and have a two-game lead on the second wild card.
Greinke will likely need to be sharp with Jeremy Hellickson (5-6, 3.42) on the mound for Tampa Bay (52-49).
Although Hellickson is 1-6 in his last 10 starts, he has allowed three runs or fewer eight times during that span. He earned his first win in over two months Tuesday at Baltimore, yielding a homer and two other hits over 6 1-3 innings of a 3-1 victory.
The right-hander surrendered a solo homer to Vernon Wells in six innings of a 3-2 win over Los Angeles on April 25.
Rays manager Joe Maddon has total confidence in his pitcher even matched up against Greinke.
"Jeremy Hellickson, to me, is one of the better young pitchers in the game also," Maddon told the Rays' official website. "He has not won a Cy Young yet, but I'll take Helly. And my point is do not underestimate what we have either."
Tampa Bay pitchers have compiled a 1.93 ERA in the last nine games, but the offense has averaged 3.4 runs and batted .223 in that stretch.