The 38-year-old was named caretaker manager in February following the dismissal of Claudio Ranieri.
Although he failed to steer Fulham away from relegation, the club commended his positive impact and expressed confidence in his ability to help the Cottagers return to England's top flight.
"Scott was brave to accept a very difficult challenge in February when appointed as our caretaker manager," Fulham owner Shahid Khan said. "Since that time, day by day, whether in training or on matchday, we’ve undeniably become a better football club.
"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."
Parker, who spent the final four years of his playing career at Craven Cottage, said he hopes to close out the season on a high when Fulham square off against Newcastle United on Sunday.
"The players, staff, and fans have all been fantastic with me since I took temporary charge," Parker said. "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, which have already begun."
Fulham returned to the Premier League this season following a four-year absence. Their relegation back to the Championship was confirmed on April 2.