Germany forward Mueller scored five times for Germany at SA2010, and was joint top scorer alongside Wesley Sneijder, Forlan and David Villa.
But he won the prestigious prize because he had more assists than the other three.
He follows in the footsteps of fellow Germans Miroslav Klose and Gerd Muller.
However the 20-year-old was denied an astonishing hat-trick of gongs after Uruguay's Forlan was awarded the Golden Ball, his goals helping the South Americans to their first semi final for 40 years.
It is the first time since 1994, when Hristo Stoichkov and Oleg Salenko scored six times, that there has not been a single highest goalscorer at a World Cup.
The only other time there was a tie was in 1962, when five players - Garrincha Vavá, Leonel Sánchez, Dražan Jerković, Valentin Ivanov and Flórián Albert, netted four times each.
On Sunday night, neither Sneijder nor Villa could add to their goal tally as Spain and the Netherlands were separated by an Andres Iniesta strike.
After winning the Golden Boot, Mueller was an obvious choice for best young player, beating off competition from Giovani Dos Santos of Mexico and Andre Ayew of Ghana.
"The honour will be with me for all time," said Mueller of his Best Young Player award.
"It's a terrific confirmation of the work I've put in over the last year, and it's a huge honour to be part of a group including the likes of Beckenbauer and Pele.
"It also points to the excellent quality of our youth development work in Germany, so I'd like to take this opportunity to thank all the staff at Bayern Munich and the Germany national set-up, and the coaching team, who have always kept faith with me. I've really enjoyed my football with the lads here."
Forlan was equally delighted with his triumph, dedicating the win to the whole of Uruguay.
"It's as great as it is unexpected," he said.
"I never even imagined something like this, nor did I have my sights set on it. As I'm a striker, I perhaps could have seen myself chasing the Golden Shoe, and in fact I came close.
"That would have been more normal. But to go from that to winning the prize for the best player... I'm enjoying it and I'm delighted, but I'm very aware that it's the result of the spectacular tournament the team has had. It's another reward for this positive period for Uruguayan football."