The 19-year-old daughter of former Republican vice presidential candidate and former Alaska Gov. Sarah Palin earlier this month called off her re-engagement to the 20-year-old Johnston.
On Friday, Palin family attorney Thomas Van Flein confirmed a report that the couple have agreed on custody. He says Palin gets primary physical custody of the little boy and they share legal custody, subject to her resolution if they can't agree.
The lawyer adds that Johnston gets visitation on Wednesdays and Saturdays.
Van Flein says Johnston will pay child support based on anticipated earnings of $72,000 per year.
A report of the agreement appeared on TMZ.com.
The couple broke off their first engagement soon after Tripp was born in December 2008.
They ended their second only weeks after it was announced.
Bristol told People magazine what happened this time.
Real Reason for Latest Bristol, Levi Split?
Levi Johnston: Mayor of Wasilla, Alaska?
Betsy Gleick, People's executive editor, said to CBS News, " is that, on the very day that the world learned they were going to get married, Levi came home and said to her that he may have gotten another woman pregnant."
Bristol said in People that the final straw came when Levi was spending more time trying to get a reality show than being a father. She said, "He's just obsessed with the limelight and I got played."