Anaheim has declined to match the US$21.25-million, five-year offer sheet Penner signed with Edmonton last week.
The Ducks will receive a first-, second-, and third-round draft pick in 2008 as compensation.
Penner scored 29 goals and had 16 assists for 45 points in his first full NHL season.
The 24-year-old was an undrafted U.S. college player that signed with Anaheim as a free agent in 2004.
He's the first player to switch teams as a result of an offer sheet in a decade, after Tampa Bay declined to match the offer Philadelphia gave to Chris Gratton in 1997.
Last month, the Oilers signed restricted free agent Thomas Vanek to a $50-million, seven-year offer sheet, but the Buffalo Sabres matched.