The two-time World Champion made it four televised titles for the year thanks to a series of spectacular displays throughout the weekend at The Brighton Centre as he clinched the £100,000 top prize.
Anderson avenged his 2017 Champions League final defeat to Mensur Suljovic with an 11-4 triumph in the semi-final before seeing off his fellow Scot by the same scoreline in the final.
Having survived two missed match darts against Michael van Gerwen in their final group game earlier in the day which would have eliminated the World Matchplay winner, Anderson recovered to fire in three ten-darters during a dominant display in the final.
"I'm over the moon to win, it was a hard weekend and I struggled at times but came good in the end," said Anderson, who has also won the UK Open, World Matchplay and US Darts Masters in 2018.
"I just turn up and play my game but it's going alright so far this year. It's been a good weekend."
Anderson also landed seven perfect darts in his bid for a nine-darter which would have earned the Brighton crowd a share of a £50,000 prize offered by sponsors Paddy Power.
"I had a good go at the nine-darter, I really tried for the fans all weekend," he added. "Now I'm looking forward to having a few days at home - my little man [son Tai] will love this trophy!"
Anderson flew out of the blocks in the final, breaking the Wright throw three times as he raced into a commanding 6-1 lead.
Wright, who came from 8-5 down to defeat Van Gerwen 11-9 in the semis, fought hard to stay in the game but a 4-7 deficit was as close as he came to halting his World Cup of Darts teammate's march to glory.
Anderson reeled off the next four legs in typically quick fashion, ending the game with three ten-dart legs and a 65% checkout rate to land his maiden Champions League title.
Despite falling at the final hurdle, it was a positive weekend for Wright, who had previously failed to make it out of the group stage in the previous two years of the event.
"I think I just ran out of steam," Wright admitted. "I played really well but I had nothing left in the final.
"Gary is the man to beat at the moment and I believe I lost to the best player of the weekend.
"It was a pleasure to play in front of such an amazing crowd."
Sunday afternoon's final group matches had seen Wright join Suljovic in progressing from Group B with a 10-3 win over World Champion Rob Cross.
A disappointed Cross said: "I didn't play anywhere near my best. I was so determined to play well but it didn't happen for me.
"It wasn't good enough this weekend and I've got to take it on the chin. We've got lots of big events coming up and I know what I've got to work on to put it right."
Northern Ireland's Daryl Gurney, meanwhile, agonisingly missed out in Group A, with his 10-7 win over Dave Chisnall coming in vain when Anderson edged past Van Gerwen by taking out 140 in the deciding leg of their contest.
Gurney conceded: "I couldn't have done much more. I gave it my all and to win two games out of three in a group like that is a good achievement."
Focus on the PDC circuit now moves to the Unibet World Grand Prix, which will be played at the Citywest Hotel, Dublin from September 30-October 6 and will be shown live on Sky Sports with tickets available at www.ticketmaster.ie.
Paddy Power Champions League of Darts
Sunday September 23
Final Group Games
Mensur Suljovic 10-1 Simon Whitlock (B)
Peter Wright 10-3 Rob Cross (B)
Daryl Gurney 10-7 Dave Chisnall (A)
Gary Anderson 10-9 Michael van Gerwen (A)
Gary Anderson 11-4 Mensur Suljovic
Peter Wright 11-9 Michael van Gerwen
Gary Anderson 11-4 Peter Wright
Written by Josh Phillips