"Any time you can add a person of his quality to your staff, it makes your organization better," Ducks GM Bob Murray said in a statement. "We've had success working together before and look forward to doing it again."
Burke was fired just days before the start of the lockout-shortened season, a surprise move by the Leafs despite the fact the team had never reached the playoffs during his four seasons at the helm.
He had remained with Toronto as a senior adviser until his hiring by Anaheim.
"Brian and I discussed this opportunity after Anaheim approached the Leafs for permission to speak with him about a possible scouting role," said Tom Anselmi, president of Maple Leaf Sports and Entertainment. "We both agreed that taking this role with Anaheim would best position Brian for his next general manager opportunity in the League."
Burke returns to Anaheim where he had more success than in Toronto as the Ducks' executive vice-president and GM from 2005-08. Over his three-plus seasons with the organization, the Ducks captured their first Stanley Cup in 2007.
The Ducks also qualified for the post-season in all three seasons, winning six of eight playoff series over that span.
Burke was named president and GM of the Leafs on Nov. 29, 2008.