Two people were killed in the first blast, and a total of seven people were wounded.
The explosions in La Paz on Tuesday night and early Wednesday, which also severely damaged the hotels, were "a case typical of terrorist crime", police commander Oscar Nina said.
Two people - an American and a Uruguayan - were arrested early on Wednesday in connection with the bombings, La Paz district attorney Jorge Gutierrez said.
Officials are unaware of the possible motives behind the explosions but believe the two foreigners were directly responsible, Gutierrez said.
The explosions occurred in the historic city center in two low-cost hotels.
The fatalities were caused by the first explosion, Nina said. Police managed to evacuate the second hotel before the blast there, he said.
"The theory we're working on is that both cases are related because bombs were placed inside" the hotels, Nina told reporters.