World champion Anderson appeared to have made a decisive move in an epic encounter when he took out 101 to move within a leg of glory.
But Dutchman Van Gerwen then played four superb legs to snatch the title from the brink of defeat.
The reigning champion had earlier missed double 12 to complete a nine-darter in the fourth leg but he went on to claim a 4-3 lead, only for Anderson to reel off four maximums in as many legs, as he took four in a row to pull clear.
Finding himself needing four straight legs himself to avoid defeat, Van Gerwen produced a pair of 14-dart legs and then levelled the match at 10-10 when a ninth maximum of the final helped him to complete a 13-darter.
The title came down to a deciding leg and, when Anderson failed to take out 134, the world number one stepped in and finished off 75 to cap another 14-darter and clinch the title in dramatic fashion.
"It's very special, especially the way that I won," said van Gerwen, who averaged 107.28 in the final and 105.58 for the tournament.
"Gary was playing fantastic darts and I couldn't find a way to put him under pressure because his scoring power at the right moments was fantastic.
"I was waiting for a mistake and when you get a chance you need to take it with both hands, and that's exactly what I did. I fought for everything but I still don't know where that finish came from.
"At 10-7 I won a leg on my own throw to make it 10-8, and then I knew it was now or never and I broke his throw, and I had a little feeling then that I was going to win.
"Maybe I played the four best legs of my career under this pressure and I'm really happy with that. It's fantastic to win a tournament like this in that way."
Van Gerwen had earlier defeated Dave Chisnall 10-4 in the quarter-finals before an 11-7 win over Peter Wright earned him a place in the final.
In the most exciting of the quarter-finals, Adrian Lewis withstood a brilliant Phil Taylor comeback to triumph 10-9.
Taylor came back from 9-6 down to level and averaged 106.12 in the match but Lewis hit tops to take the deciding leg, only to lose 11-5 to Anderson in the semis.
European Championship 2015: Daily Results
Friday October 30
Afternoon Session (1245-1700 GMT)
First Round (best of 11)
Cristo Reyes 6-2 Max Hopp
Christian Kist 4-6 Rowby-John Rodriguez
Simon Whitlock 6-2 Magnus Caris
Justin Pipe 6-2 Dirk van Duijvenbode
Michael Smith 6-4 Gerwyn Price
Ian White 5-6 Stephen Bunting
Robert Thornton 4-6 John Henderson
Peter Wright 6-3 Alan Norris
Evening Session (1900-2300 GMT)
First Round (best of 11)
Adrian Lewis 6-5 Benito van de Pas
Mensur Suljovic 5-6 Dave Chisnall
James Wade 6-3 Terry Jenkins
Gary Anderson 6-3 Brendan Dolan
Jelle Klaasen 6-4 Raymond van Barneveld
Phil Taylor 6-1 Vincent van der Voort
Michael van Gerwen 6-3 Jeffrey de Zwaan
Kim Huybrechts 6-3 Mervyn King
Saturday October 31
Second Round
Afternoon Session (1245-1700 GMT)
John Henderson 10-2 Rowby-John Rodriguez
Stephen Bunting 6-10 Dave Chisnall
Adrian Lewis 10-7 Justin Pipe
Gary Anderson 10-8 Simon Whitlock
Evening Session (1900-2300 GMT)
Peter Wright 10-8 Kim Huybrechts
Phil Taylor 10-5 Michael Smith
Michael van Gerwen 10-3 Cristo Reyes
James Wade 5-10 Jelle Klaasen
Sunday November 1
Afternoon Session (1245-1700 GMT)
Quarter-Finals (best of 19)
John Henderson 4-10 Peter Wright
Michael van Gerwen 10-4 Dave Chisnall
Gary Anderson 10-6 Jelle Klaasen
Adrian Lewis 10-9 Phil Taylor
Evening Session (1900-2300 GMT)
Semi-Finals (best of 21)
Peter Wright 7-11 Michael van Gerwen
Gary Anderson 11-5 Adrian Lewis
Final (best of 21)
Michael van Gerwen 11-10 Gary Anderson