Midfielder Pringle is a free agent after leaving Rotherham and goalkeeper Lonergan ended a three-year stay at Bolton at the end of last season.
Both players agreed two-year contracts and will officially become Fulham players on July 1.
Pringle, 26, told the club website: “I’m buzzing. As soon as I knew that there was interest from Fulham I wanted to come here straight away.
“You just have to look at the size of the club and where they’ve been in the past – hopefully we can get there again before too long.
“I like to think I’ll bring energy to the team. I try to make things happen, I can cross a ball okay and try to get in little pockets.”
Former Preston and Leeds keeper Lonergan, 31, said: “I’m delighted to get it all sorted. I’m happy to be here and I can’t wait to get started.
“It’s a very well respected, historic club and it’s a place where everyone would like to play. We have a lot of potential to hopefully get back to where the club belongs.”