Stewart, 43, agreed to take one of entertainment's most desirable MC jobs just before Christmas. Stewart has twice hosted the Grammy awards.
The Times said Stewart will take at least a week off from "The Daily Show" to prepare for the awards ceremony.
The Academy Awards show's producer said Stewart has many of the qualities of previous masters of ceremonies.
"Jon is the epitome of a perfect host — smart, engaging, irreverent and funny," producer Gil Cates said.
Four nights a week on Comedy Central, Stewart presides over "The Daily Show with Jon Stewart," a comedy show that masquerades as journalism, deconstructing the day's events and the pretenses of television news by repackaging reality as a parade of the absurd.
"The Daily Show" has earned seven Emmys and a Peabody award. He has previous experience hosting awards shows, taking over the Grammys in 2001 and 2002.
He won the 2005 Thurber Prize for American Humor for his book, "The Daily Show with Jon Stewart Presents America (The Book): A Citizen's Guide to Democracy Inaction" and has appeared in movies including "The Faculty," "Death to Smoochy" and "Big Daddy."
"As a performer, I'm truly honored to be hosting the show," Stewart said, then joked: "Although, as an avid watcher of the Oscars, I can't help but be a little disappointed with the choice. It appears to be another sad attempt to smoke out Billy Crystal."
Stewart follows a long line of standup comedians who have hosted the Oscars. Over the years, Bob Hope, Johnny Carson, Whoopi Goldberg and Crystal have held down the podium.
Speculation has swirled over who would replace Chris Rock as host. Frequently mentioned candidates included Goldberg, Steve Martin and late-night hosts Jay Leno and Conan O'Brien. The nod to Stewart was first reported on the Los Angeles Times' entertainment awards Web site theenvelope.com.
"Jon is the new guy and I believe he's going to fit in perfectly with that group," said Academy President Sid Ganis. "He's a very, very popular entertainer with a mind that is quick, and you need that on a show like this."
Rock drew younger viewers, but his barbs skewering stars like Jude Law, Tobey Maguire and others alienated some academy members. Rock is currently producing and narrating "Everybody Hates Chris," a UPN sitcom based on his life.
The 78th annual Academy Awards will air March 5 on ABC from Hollywood.