Following on from that Serena is set to make her long-awaited return to the Australian Open in mid-January, after sitting out the tournament previous year to recover from giving birth.
Federer spoke about how much he enjoyed the experience, saying: "It was great fun".
In the encounter's first match Greek champion Tsitsipas beat American Frances Tiafoe 6-3 6-7 (3) 6-3, before Williams, in her first competitive action since the US Open final, saw off Sakkari 7-6 (3) 6-2 to level the Group B contest at 1-1.
Before the match Williams had talked of wanting a selfie with Federer post match and the pair had their special moment after the game, posing together on the court with a selfie-stick.
"It was so fun".
"So it just goes to show you how we as players come so far in our careers and we still have other lives that mean so much to ourselves", she added.
"I felt a bit uncomfortable in the first match I played". Thanks for making this match possible.
Williams and Federer, both 37, faced off in a mixed-doubles exhibition match at the Hopman Cup on Tuesday.
Image Frances Tiafoe and Williams took on Federer and Belinda Bencic at the Hopman Cup
Defending champion Switzerland will qualify for Saturday's final if it beats Greece on Thursday.
The much-hyped contest lived up to the billing immediately with Federer nearly running down Williams' smash into the open court.
Williams felt the same about facing Federer, and also heaped compliments on his serves.
Federer and Williams, of course, won't be the only players on the court in a mixed doubles match.
Williams grabbed at her right shoulder several times during the match, but said it wasn't anything to worry about.
"It was such a quick turnaround, I didn't have enough time to reload the cannon. This is so cool", she said.
Federer and Bencic will next take on Williams and Frances Tiafoe to kick-start the New Year with arguably the most anticipated match in the tournament's three-decade history. The 20-time Grand Slam champion moved around the court well and hit the ball crisply to overwhelm Norrie. "What an honour", 20-time Grand Slam victor Federer said after the match.
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