The specifics were not revealed, but Russian Presidential Aide Yuri Ushakov said details of the upcoming summit will be announced by U.S. and Russian officials Thursday, CNN reported.
Helsinki, Finland, and Vienna, Austria, have been mentioned as possible summit sites.
"The two countries have discussed the [summit] issue for a long time, it has been discussed through closed channels," Ushakov said. "I can say that an agreement has been reached on holding the summit, even an agreement on the time and venue. We will presumably announce that tomorrow together with our U.S. counterparts."
Putin and Trump will meet in a "comfortable" venue in a third-party country, he said. CNN's report also cited a U.S. official confirming the agreement. The Washington Post reported Bolton confirmed the deal.
Ushakov added the summit would likely last for several hours and include some kind of working breakfast and joint news conference.
On his visit to Moscow, Bolton also met with Russian Foreign Minister Sergey Lavrov, foreign policy adviser Yuri Ushakov and members of Russia's Security Council.
"In our bilateral relations, we cannot boast of intense bilateral contacts, let alone high-level ones, that's why certainly, such contacts are used for exchanging views on key global issues -- they are rather clear and evident," Kremlin spokesman Dmitry Peskov said.
Peskov said the meeting might be used to discuss "the sad state" of bilateral relations between the United States and Russia.
The meeting may follow Trump's trips to a NATO summit in Belgium on July 11 and Britain two days later.