Having spent last season on loan at Craven Cottage, Reed has joined permanently this time round on a four-year contract, with Fulham having the option to extend the deal by a further year.
Fulham have paid Southampton £6m for Reed, who made 28 appearances in the championship last season to help the Cottagers gain promotion to the English top flight.
Having sealed his return, Reed told FFCtv: "I'm absolutely buzzing to finally get it done and to be here as a permanent player, I'm absolutely over the moon.
"It's going to be an exciting season, it's a big challenge this year, but I can't wait to get going, to get back training, and I'm really looking forward to the challenge. I'm absolutely delighted to be here and commit my future to the club."
Lemina joined Southampton from Juventus for £18m in the summer of 2017 but spent last season on loan at Turkish giants Galatasaray.
The 26-year-old Gabon international’s temporary switch will be made permanent if Fulham are able to avoid relegation.
Speaking after completing his loan switch, Lemina said: "Now I'm with Fulham, I'm really happy and I'm glad to be part of the project.
"I spoke with the manager and he's got some good ideas about the team, about the project, about everything he wants to do this season, and I'm happy to be a part of it."
Fulham will begin their Premier League campaign with a home game against Arsenal on September 12.
