The final form of the deal sends Neal and Ridnour to Charlotte for Sessions and Jeff Adrien.
The Bobcats confirmed the deal Thursday evening.
"We are excited to add a pair of quality players to our backcourt," Bobcats president Rod Higgins said in a statement. "Gary is an exceptional shooter and Luke is a veteran point guard who can help us off the bench."
The Bobcats (who at 25-30 are in eighth place in the Eastern Conference) have been chasing the disgruntled Neal for some time, but Milwaukee balked at a pure Neal-for-Sessions swap because Sessions is making $5 million this season, compared to Neal's $3.25 million. Adding Ridnour to the trade puts the financial onus back on Charlotte.