Pouille defeated Denis Istomin of Uzbekistan 6-4, 6-7 (5), 6-3, and Raonic upset the third-seeded Tomas Berdych 7-6 (2), 7-6 (1).
The 36-year-old will regain the world number one ranking on Monday and is playing next week as top seed in Halle.
He could go to 150 points if he wins against Milos Raonic in Sunday's final.
Federer also won their quarterfinal a year ago at Wimbledon while Raonic took their 2016 semifinal meeting at the All-England Club. I've come back from not playing the last few weeks and I've come back playing at a high level.
In the process, he earned 150 points, taking him above Rafael Nadal in the ATP rankings to return to the summit for the sixth time in his legendary career. I just hope to stay injury free and healthy.' Analyzing the final and the week overall, Federer added: 'I played great in the big moments.
"That would mean I would have to win a couple of Grand Slams in order to be No 1, especially with Roger and Rafa winning a lot of them".
Federer's 78-minute win, sealing his first Stuttgart triumph, was the flawless tonic for the Swiss in the build-up to defending his Wimbledon crown, having extended his unbeaten 12-month sequence in grass court matches to 16.
The Swiss broke twice in the first set to take it after 32 minutes when his opponent returned long over the baseline.
In a decisive tiebreak after no breaks in the second set, a double fault from Raonic at 3-4 paved the way for Federer to claim the 18th grasscourt trophy of his career. Looking ahead to the final, Federer has a 10-3 record over Raonic who hammered 19 aces past Pouille.
"The key for me is to be ready for that opening match".
After first serve percentage languished at 48% in the second set, the Australian was able to lift it to near the 80% mark for the decider, just as he'd done during the first set, to once again present Federer with a much stiffer challenge.
"It will all depend on how many matches I get next week and then I'll decide what to do in the week before Wimbledon", Raonic said.
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