In a brief statement, Williams said the 29-year-old German would be partnering Jacques Villeneuve next season - but made no mention of 1998.
It had been understood that Frentzen, who has had three seasons with Sauber, would be signing a two-year contract, but the second year may be subject to the team's discretion.
Frank Williams, the team director, also gave a three-sentence appreciation of Hill, who leads the World Championship by 13 points from Villeneuve with three races remaining.
"Damon has contributed greatly to the team both as a test and race driver - he has done an excellent job for us," Williams said. "I think his record speaks for itself, as very few drivers have ever approached his record of 20 wins in 64 starts. He will be missed by everyone at our Grove factory and we will wish him the best of luck for the remainder of this year, as well as the future."
Hill resumes his quest for the title in the Italian Grand Prix at Monza on Sunday. If he wins that race, and Villeneuve is no better than fourth, the Englishman's mission will be accomplished.
Jordan-Peugeot remain the favourites to sign the 35-year-old Hill for next season, although he has also been linked with a possible move to IndyCars.
Frentzen's arrival in Formula One's top team will have Germany's motor racing followers salivating at the prospect of his confronting Michael Schumacher.
In their earlier days, as members of the Mercedes "junior" sports car team, many rated Frentzen the quicker of the two drivers. He is, however, almost two years older than Schumacher, who developed rapidly and was more dedicated to his job.
Frentzen was more laid-back, enjoyed life beyond the race track and was left behind by Schumacher, Germany's idol, and Frentzen's girlfriend joined the flow, eventually becoming Mrs Schumacher.
Born in Monchengladbach, Frentzen had a familiar grounding, starting in karts, becoming the German junior champion, and graduating to cars. He advanced through Formula Ford 2000 and Formula 3 to join Eddie Jordan's Formula 3000 team, as well as the Mercedes organisation.
While Schumacher was emerging as the new golden boy of Formula One, Frentzen was plying his trade in Japanese Formula 3000 and sports car championships.
His break in Formula One came in 1994, when he returned to the Sauber- Mercedes camp for their assault on motor racing's premier category. However, Mercedes switched to McLaren after the first season and Sauber have failed to make a significant impact.
Frentzen's best result is third place, ironically at Monza last year, but presumably he has shown sufficient potential to assure Williams he is worthy of their car.
He is patently fast and his erratic form this season may have more to do with frustration than true ability. If he is good enough, he will have no need to drive over the limit next season.
All Germany will be watching with fascination - and probably no one with greater interest than Schumacher.Reuse content