Fry worked at the team in its Benetton days from 1987 to 1993, before embarking on a career that encompassed two spells at McLaren, and one at Ferrari.
He returned to the Enstone camp in 2020, but after contributing to the last three cars he decided to leave earlier this year.
By a coincidence of timing, his move to Williams became public on the same day that the sudden departures of team principal Otmar Szafnauer and sporting director Alan Permane were announced.
After a short gardening leave, he began work at Grove earlier this month.
Speaking for the first time since he left Alpine, Fry said the team made good progress during his stint there, but he sensed that further steps would be harder.
"I look back at the first three years I was there, and we improved Enstone, dramatically," he said when asked by Autosport to explain his move. "Year-on-year, we built a better car.
"If you put the three cars next to each other, each one was a massive step. It's a credit for everyone there, the various teams were collaborating a huge amount better. I think everyone there should be proud of what we achieved for those three years.
"I guess I'd gone back there [thinking] to go back to the place you started your career and try and rebuild it. And I think we did really well. From a distant fifth, we were a solid fourth.
"But I didn't feel there was the enthusiasm or the drive to move forward beyond fourth.
Source: Autosport