The high rise residential condominium and spa, named Palms Place, is scheduled for completion in 2007.
Lachey and Simpson cited their love for the city and George Maloof's Palms Property as motivation for the purchase.
"George is going to have a two story basketball suite, which is down the hall from a multimillion dollar state of the art recording studio there ... so I'm there," Lachey said.
The couple, who recently completed the third and final season of "Newlyweds," were both working on new solo albums Wednesday. Lachey was also preparing for his own MTV show, "The Nick Lachey Project," slated to premier this summer. Simpson will be seen next in the upcoming feature film, "The Dukes of Hazzard."