Jackson takes over a team that has performed well below Dolan's expectations this season. New York is 13 games under .500 and in ninth place in the Eastern Conference, though the team has won six in a row.
Jackson will face several tough decisions in his first offseason as president, the biggest of which is what to do with free agent-to-be Carmelo Anthony.
The team's new president backed the All-Star forward Tuesday.
"There's no doubt about Carmelo being one of the top scorers in the league, maybe the best individual isolation player in the game," Jackson said. "I have no problems with committing to saying Carmelo is in the future plans."
Anthony, who has said he plans to opt out of the final year of his contract this summer, can sign a deal with the Knicks that is one year longer and worth $33 million more than any pact he can sign with another team. He has said that his priority is to re-sign with the Knicks, but he would like to sit down with Jackson and discuss the team's plans before making a decision.
Jackson also will likely have to hire a coach in the offseason. There is widespread speculation that Mike Woodson will be let go at the end of the season. Jackson disciples such as Steve Kerr, Brian Shaw and Kurt Rambis are considered potential candidates.
Regarding Woodson, Jackson said the two will have discussions about the coach's future in the coming weeks but made no guarantees that he'll be back next season.
One thing Dolan would guarantee for next season: Season-ticket prices won't be raised, he said.
Jackson's fiancee, Lakers president Jeanie Buss, knew Jackson was ready for a new challenge.
"It was clear that Phil wanted to go back to work," Buss said in an interview with Time Warner Cable SportsNet. "He'd spoken to different organizations. Me personally I like having Phil around. But there was no role for him with the Lakers. He's too good of a basketball mind to sit at home in a rocking chair playing solitaire."
One person outside of New York especially happy to see Jackson's return to the NBA is Dallas Mavericks owner Mark Cuban.
"My bucket boy is back," Cuban said jokingly, bringing up his favorite term for Jackson during the verbal sparring sessions when Jackson coached the Lakers.
Cuban added: "It's great just because of the legacy, the pedigree, the questions. Can he do it again? He's won everywhere he's gone, including his first stop in New York, so can he do it again?"
Tuesday's announcement brought Jackson back to the city where his playing career started.
He recalled his first trip into New York as a player in 1967. Coach Red Holzman and his wife, Selma, drove Jackson from Kennedy Airport to Manhattan. The trip was interrupted when someone on a highway overpass threw a rock that cracked Holzman's windshield.
"Red looked up and said, New York isn't the easiest place to live," Jackson said with a laugh. "But if you can make it here, you can make it anywhere. That is where the phrase started. I swear. So we are going to make it here."
Information from ESPN's Ramona Shelburne and ESPNDallas.com's Tim MacMahon was used in this report.