The Bucks also have the option of switching first-round picks in this year's draft, provided the Bulls' pick isn't in the top 10. The Bulls added second-round draft choices in 2011 and 2012.
"We had flexibility going into this summer already with some of the things we've done in the past, but in order to create the cap space to attract a max free agent this summer, we knew we had to make some moves," Bulls general manager Gar Forman said. "And like a lot of teams, we positioned ourselves to be able to attract a maximum free agent this summer.
"We created that flexibility, which was important. In doing so, we created that flexibility without tearing into the nucleus of our players, of our team. That was important to us, that we kept the nucleus of guys we had: Derrick Rose, Joakim Noah, Luol Deng, Taj Gibson, Kirk Hinrich; that we kept that group together."
Warrick is a 6-9 power forward who is averaging 10.2 points and 4.4 rebounds. The Syracuse product was the No. 19 overall pick by the Memphis Grizzlies in 2005.
Alexander, the eighth overall pick in 2008, has battled a hamstring injury this season.
Salmons has a $5.8 million player option for next season that the Bulls didn't want to deal with as they clear space to be a major player in free agency this summer. Salmons will fill in for injured shooting guard Michael Redd.
"He's a good pro guard," Bucks coach Scott Skiles said of Salmons. "He's been a solid player for quite a while, and we feel like we still need to solidify one of our perimeter spots, especially with Michael out. So it made sense."
"We have had issues at times, especially starting games -- how can we find ways to score points if by chance Andrew [Bogut] isn't scoring early or Brandon's not having the chance to hit some early shots," Hammond said. "We've had difficulty. And once again, I think John's the kind of player that's proven he can score."
The Associated Press contributed to this report.