It marked the third time this season that Marco Silva's Premier League-bound side have netted seven goals.
The full-time whistle on Monday was followed by a pitch invasion at Craven Cottage as selfie-hunting fans mobbed the players before they were ushered off for the trophy presentation.
The London club became the first team in two decades to score more than a 100 goals in a single season in the second tier as six different players found the back of the net against Luton.
Captain Tom Cairney opened the scoring in the 29th minute and Kenny Tete made it two 10 minutes later. The floodgates opened in the second half with goals from Fabio Carvalho, Bobby Decordova-Reid, Jean Michael Seri and a brace from Aleksandar Mitrovic.
The Serbian striker has now scored 43 goals in 43 games this season - the most in a season at this level since Brian Clough hit 43 in 42 matches for Middlesbrough in 1958-59.
"To do it at home in front of your fans, to be champions of the league -- no matter whatever league, whatever standard -- that lives forever," said Tom Cairney, who scored the opener which was also Fulham's 100th goal of the season.
"We create a hell of a lot of chances... It also tells you about a person (Mitrovic) who is a special talent -- 43 Championship goals is astounding. He deserves all the plaudits, he's a top, top striker."
The margin of the defeat could have repercussions for Luton Town who had to field emergency loanee Matt Ingram in goal in place of the injured James Shea.
They are in the sixth and final playoff spot but their goal difference is now inferior to the two clubs behind them: Middlesbrough, two points behind, and Millwall, a point further adrift.
With PA
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