"The players, staff and fans have all been fantastic with me since I took temporary charge," said the former England midfielder.
"We are now all focused on ending this campaign with a positive result on Sunday against Newcastle and look forward to preparations for the new season."
Former club captain Parker, 38, returned to Craven Cottage as first team coach in 2018 before being installed as caretaker manager following Claudio Ranieri’s departure in February, but he could not prevent their relegation to the Championship.
He made 128 appearances for the London side as a player between 2013 and 2017.
Fulham chairman Shahid Khan said Parker had been brave to take on the role of caretaker boss.
"Since that time, day by day, whether in training or on match day, we’ve undeniably become a better football club," he said.
"Scott will now have another challenge to face, and that is to return Fulham to the Premier League. I fully believe Scott is more than up to the task."