The 21-year-old will serve as back-up to Number One David Forde and will provide competition for Preston Edwards.
"It is a great chance to come to a big club like Millwall," Sullican told the club's official website. "Hopefully next year we can try and have another go at getting back to the Championship.
"I'm excited at the prospect of trying to get into the team next year."
Sullivan will officially sign when the transfer window reopens on July 1st.