Federer produced another of the supremely dominant displays he seems to reserve for this tournament as he cruised past Murray in one hour and 33 minutes at London's O2 Arena.
The Swiss great is now one win away from completing a hat-trick of titles at the prestigious season-ending event.
While the two venues couldn't be more different, the 17-time Grand Slam champion seems just as in his element under the O2 Arena's domed roof as he does on Wimbledon's Centre Court.
Murray pushed him hard in the first set, but once Federer got into his stride the result was inevitable as the 31-year-old emulated his Wimbledon triumph over the Scot and in the process gained a measure of revenge for losing their Olympic final clash.
Murray, who was bidding to become the first Briton to reach the final, has enjoyed a year to remember, but this was a frustrating way to end it as he bowed out in the semi-finals for the third time.
"It was a special match," Federer said.
"It was the third time in London this year for the two of us and the crowd was electric," he said.
"I have been around the block a few times and that was something — you can't tire of nights like this," Federer said.
"That is why I keep practising in front of no people, it inspires you to keep working hard."
In his gold medal victory at the All England Club, Murray had set the tone for his straight sets win by grabbing the initiative from the start and he was clearly determined to do the same again.
Taking the attack to Federer, the 25-year-old earned two break points in the first game of the match and converted the second with a blistering winner.
But, rather than triggering a period of Murray dominance, that was simply the cue for an absorbing battle to break out.
Federer was in a more determined mood than during his Olympic defeat and the world number two kept probing away at the Murray serve, eventually earning his reward with a break to level at 4-4 after a searing backhand proved too hot for the Scot to handle.
To his credit, Murray refused to cede any further ground after that and a tie-break was required to settle the set.
It was the same story in a tremendously tense breaker.
Murray had the early advantage, but couldn't kill off Federer, who broke back after a 22-shot rally.
Federer then seized the moment, wrong-footing Murray with a looping forehand at 6-5 to seal the set in 61 minutes.
With the momentum firmly in his favour, Federer was able to unveil the full range of his arsenal in the second set.
Rather than try to over-power Murray, he teased him with a series of backhand slices and drew a frustrated mistake from the Scot that gave Federer a break for a 2-1 lead.
Federer was even more energised by that vital breakthrough, while Murray seemed to lose all belief and it wasn't long before the Swiss delivered the final blow when he broke again to move 5-2 ahead before serving out the win.