Bach and his board have come to their decision after reading through the findings and recommendations of a 17-month investigation headed by the former president of Switzerland, Samuel Schmid.
Some of the country's athletes will be allowed to compete under the tag of "Olympic Athlete of Russia", if they satisfy strict conditions that show they have a doping-free background.
The IOC stopped short of that, instead saying that some Russian athletes will be permitted to compete in Pyeongchang under a specially created status, "Olympic Athlete from Russia (OAR)", according to the IOC statement.
They will compete with a uniform carrying that name, while the Olympic anthem - and not the Russian one - will be played at any medal ceremony.
Tatyana Tarasova, a prominent Russian figure skating coach, said the International Olympic Committee decision was "absolutely unjust". Schmid's report confirmed "the systemic manipulation of the anti-doping rules and system in Russian Federation". In the 2014 Winter Games in the Black Sea resort of Sochi, Russia led the medal count, with 33 overall and 13 golds.
The IOC also fined the Russian committee $15 million to pay for the doping investigation.
"This was an unprecedented attack on the integrity of the Olympic Games and sport".
In an embarrassment for Russia's hosting of the 2018 World Cup, the International Olympic Committee also banned Russian Deputy Prime Minister Vitaly Mutko from the Olympics for life.
The president of the Russian skating union has described the decision of offensive and insulting.
The neutral-athlete sanction is based on the approach taken by athletics' world governing body the IAAF at the Rio Games in 2016 and at this summer's World Championships in London.
But all eyes will be on President Vladimir Putin on Wednesday when he is scheduled to speak to his supporters during a planned event.
"This should draw a line under this damaging episode and serve as a catalyst for a more effective anti-doping system led by WADA", he added, referring to the World Anti-Doping Agency.
Some had feared a repeat performance from the International Olympic Committee on Tuesday, despite a second report by McLaren in December 2016 which confirmed that more than 1,000 Russian athletes had been involved in, or benefited from, state-sponsored doping. "There were no ideal options, but this decision will clearly make it less likely that this ever happens again", it said.
In his affidavit, Rodchenkov said: "I know I have disappointed many friends and colleagues with my duplicity while serving as director of the Moscow lab". The sanctions have knocked Russian Federation down to fourth place in the medals table after finishing first in 2014 with 33 medals.