Boca lost 3-1 after extra time in last Sunday's second leg in Madrid to go down 5-3 on aggregate. It was the first Copa Libertadores final between the Buenos Aires rivals.
The final was twice postponed and eventually played in Spain because of violence caused by River fans in Buenos Aires.
"The best thing for Boca is to start the year making a change — search for a new coaching staff and start all over from scratch," Boca president Daniel Angelici told a news conference.
Schelotto, whose contract was due to end on Dec. 31, spent the majority of his 16-year playing career at Boca, winning three Copa Libertadores titles and scoring 86 goals.
"Despite not winning the Copa Libertadores, I leave at peace knowing that I left it all on the field," the 45-year-old former striker said. "This is the best decision we could have taken."
Under Schelotto, Boca won the Argentine league title for the past two seasons and currently sit sixth in the standings.
Among the names already linked with the job are Gustavo Alfaro, coach at Huracan, ex-Manchester United defender Gabriel Heinze, currently in charge at Velez Sarsfield, and Miguel Angel Russo, who led Boca to their last Libertadores title in 2007.
"I know the world of Boca and that is key," Russo told Fox Sports. "It's a demanding job because the club is one of the biggest in the world. I am cautious but I'd be delighted if they called."
Jose Pekerman, who managed Argentina after a successful stint as the country's youth coach in the 1990s, is another who could interest Boca, having parted ways with Colombia after leading them to this year's World Cup in Russia.
(Reporting by Hardik Vyas in Bengaluru; Additional reporting by Andrew Downie; Editing by Ken Ferris)
