Kleina, 44, led Ponte Preta out of Serie B last season and will leave the Campinas-based side who are 11th in the Brazilian championship to join relegation-threatened Palmeiras, who are 19th.
Former Brazil, Portugal and Chelsea coach Scolari ended his second stint with Palmeiras last week after a run of defeats left them in serious danger of dropping into the second division.
Felipao (Big Phil), as Scolari is usually known, had been at the club for two years.
Kleina's departure from Ponte Preta means there have been 25 coaching changes this season among Brazil's 20 top-flight clubs, with five in September alone.
Atletico Goianiense are the record holders having given the hot seat to Helio dos Anjos twice, Jairo Araujo, Adilson Batista and now Arthur Neto.
"We were taken completely by surprise," said Ponte Preta president Marcio Della Volpe. "We don't have a plan B because for us there was only ever a Plan A. Gilson Kleina was our coach until December 2012, at least."