The Sweden Under-21 international has signed a three-year contract with the Premiership side, with Cottagers boss Chris Coleman putting the striker up as one for the future.
Runstrom, who has previously spent time in Italy, believes moving to Craven Cottage is the best decision for his career.
"It feels good to take the step to a really good league," Runstrom told Sportbladet.
"Fulham is a perfect club. It is not too big and not too small.
"I got the impression that they truly believe in me."
The young hot shot had the chance to join Fulham during the January transfer window, but elected to stay at Hammarby.
He admits he signed a new contract with Hammarby to ensure the club received a suitable fee once Fulham returned with a fresh bid this month.
Runstrom added: "I didn't want to go on a free transfer in January, although I had an offer from Fulham already then.
"Hammarby have meant much to me and I wanted them to get well paid.
"I have had the best years of my life at the club, but I need new challenges."
SkySports