The news was confirmed in a media statement issued by the governing FIA after its Barcelona meeting on Friday.
The Paris-based body said the decision to reschedule Bahrain to October 30 this year "reflects the spirit of reconciliation" in the troubled Kingdom, following months of civil unrest.
"The World Motor Sport Council feels that reinstating the grand prix is a means of helping to unite people as the country looks to move forward", the FIA added.
A new date for India has not yet been set, but the FIA hinted strongly that it will be in December, "combined with the FIA annual general assembly and prize-giving gala" in Delhi.
Ross Brawn said in Monaco that December is "totally unacceptable" to the teams, so well-known F1 photographer Darren Heath on Friday dared the teams' group FOTA to show its mettle.
"The safety of everyone in F1 will surely be put at risk," he wrote on Twitter.
FOTA responded by saying Friday's decision will be "discussed internally" with a position to be announced later.
Also on Friday, Bahrain was announced as the season opener for the 2012 season, with the provisional calendar for next year featuring an unprecedented 21 grand prix dates.
Turkey in May, however, accompanies an asterisk warning it is "subject to confirmation", while Texas is as expected paired with Canada in June.
The FIA also reinforced the 2013 engine rules featuring four-cylinder turbos, but said the "implementation date" could be reconsidered by fax vote "by June 30 latest".
Next year, meanwhile, the cars' nose tip height will be limited for T-bone style crashes, while the minimum weight will increase to 660kg.