Summary
Andy Murray wins 6-3 6-4 in one hour 42 minutes
35th meeting between the pair
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Rally Potterpublished at 20:31 Greenwich Mean Time 20 November 2016
And from an Olympic silver medallist...published at 20:30 Greenwich Mean Time 20 November 2016
Decent supportpublished at 20:29 Greenwich Mean Time 20 November 2016
Watch again: Trophy timepublished at 20:28 Greenwich Mean Time 20 November 2016
Here's the moment Andy Murray was presented with his suitably large trophy to end an incredible year...
Media caption, Andy Murray lifts the ATP World Tour Finals trophy.
Praise from another hot-shotpublished at 20:27 Greenwich Mean Time 20 November 2016
From a former king...published at 20:26 Greenwich Mean Time 20 November 2016
Here's a question...published at 20:24 Greenwich Mean Time 20 November 2016
Brothers on top of the worldpublished at 20:23 Greenwich Mean Time 20 November 2016
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End of twitter postMarathon yearpublished at 20:22 Greenwich Mean Time 20 November 2016
Knockout!published at 20:21 Greenwich Mean Time 20 November 2016
He made it so...published at 20:20 Greenwich Mean Time 20 November 2016
Murray wins the ATP Finals & remains world number onepublished at 20:19 Greenwich Mean Time 20 November 2016
Andrew Castle
BBC Sport tennis commentator on BBC TwoThis achievement, to put in perspective, is bigger than any grand slam. It takes an awful lot of work.
Murray wins the ATP Finals & remains world number onepublished at 20:17 Greenwich Mean Time 20 November 2016
Andrew Castle
BBC Sport tennis commentator on BBC TwoI didn't think it was possible today. Murray only had 24 hours to recover after a really taxing match. The first five games were important for Murray to establish himself and when he got the break he took it. That is when the belief round here grew.
You knew Djokovic wouldn't go away without a fight but Murray found a way to get over the line.
get involved Get Involvedpublished at 20:16 Greenwich Mean Time 20 November 2016
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Robbie Devenney: Sitting in a restaurant in Venice, waiting on food, massive cheer for our table when Andy won, now getting funny looks.
Matthew Carr: Arise Sir Andy Murray! Congratulations @andy_murray, external on becoming ATP World Tour Finals champion & ending year as world number one.
Murray wins the ATP Finals & remains world number onepublished at 20:15 Greenwich Mean Time 20 November 2016
Image source, Getty ImagesAndy Murray: "It's very special playing against Novak in a match like this, we've played Grand Slam finals and Olympic finals before, but I am very happy to win and to be world number one is very special. It is something I never expected.
"My team have been around a long time, and my family have been there from the very start and made lots of sacrifices so I thank them.
"Me and Novak are lucky to have two great champions in our boxes, but to have other great champions like Mats Wilander and Stefan Edberg here today is special. To hold all four Grand Slams like Novak did this year was a very special achievement and something we won't see for a very long time."
It's in the blood, brotherspublished at 20:15 Greenwich Mean Time 20 November 2016
So. I did ask earlier this week: who will carve the Xmas turkey? Jamie or Andy? They're both world number ones.
Best let mother Judy do the duties.
Watch again: Murray's winning momentpublished at 20:11 Greenwich Mean Time 20 November 2016
Ultimate showman Murray allowed Djokovic to save a couple of match points - just because he knows we love the drama. But in the end he got the job done, here's the winning moment...
Media caption, Andy Murray defeats Novak Djokovic 6-3 6-4 and wins the ATP World Tour Finals
get involved Get Involvedpublished at 20:10 Greenwich Mean Time 20 November 2016
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Annabel Blackett: UNREAL UNREAL. JUST OUTSTANDING. @andy_murray, external Just played the match of his life.
Abbie Grisman: Number 1, number 1, number 1, number 1, number 1!!!!!!! Yes.
Dan Moloney: Huge from @andy_murray, external! What a fighter. Proud! BEST. IN. THE. WORLD!
Murray wins the ATP Finals & remains world number onepublished at 20:09 Greenwich Mean Time 20 November 2016
Novak Djokovic: "It has be a fantastic year with some great highlights, especially in the first six months. Andy is definitely number one in the world. He deserved to win. He is the best player.
"In the decisive moments I wasn't able to come back. I played better late in the match but it wasn't enough.
"I wish him and his team all the best for the year."
Image source, BBC SportMurray wins the ATP Finals and remains world number onepublished at 20:05 Greenwich Mean Time 20 November 2016
Pat Cash
Former Wimbledon champion on BBC Radio 5 live
Image source, Getty ImagesIt is amazing, he has had a phenomenal year and he deserves to be number one. Djokovic was the one that capitulated, he's not had a good six months but Murray was solid and deserved to win the trophy.