The TV and radio presenter joined the Radio 1 team last month as Fearne Cotton's showbiz and entertainment reporter.
Edmondson will host the 10am to 1pm slot, which mixes classic tracks, latest hits and entertainment news.
"I'm ridiculously excited about getting started on the 'Lie In'," said the 24-year-old. "I've been busying myself in the basement of Radio 1 HQ and have got some great stuff planned for the show - I can't wait."
Deputy controller of Radio 1 Ben Cooper added: "It's always exciting when brand new talent start on Radio 1. I'm really looking forward to hearing Matt on a Sunday morning with his particular take on the world."