The 23-year-old winger will play her football in the Women’s Super League for Hope Powell’s side for the 2021-22 campaign.
A skilful player blessed with lightning pace, Babajide has spent the last three seasons with the Reds and become a firm fan favourite.
LFC Women manager Matt Beard said: “I’ve had good discussions with Rinsola since I arrived and this is a very good opportunity for her.
“She was keen to play WSL this season and especially to be closer to her family down south.
“We’ll be following her progress with great interest and wish her well for a successful campaign with Brighton.