In addition, several U.S. B-1B heavy bombers have arrived in Britain in support of two separate multinational exercises planned in the Baltic region and other parts of Europe this month to improve coordination among partner countries, Reuters said.
The U.S. military plans were announced by Stuttgart-based U.S. European Command, which said this year's Saber Guardian exercise - held annually in the Black Sea region since 2013 - was "larger in both scale and scope" than previous exercises.
The news could exacerbate tensions that are already running high between Moscow and Washington.
Russia scrambled a fighter jet on Tuesday to intercept a nuclear-capable U.S. B-52 strategic bomber it said was flying over the Baltic Sea near its border, in an incident that had echoes of the Cold War.
Washington said the long-range bomber was operating in international airspace.
European Command said the Saber Guardian exercise would include an array of live fire exercises, river crossings and a mass casualty exercise and was aimed at drilling "the ability to mass forces at any given time anywhere in Europe".
"It is deterrence in action," it said in a release.
The U.S. army said the larger exercise would be preceded by several smaller events - all aimed at shoring up the security and stability of the Black Sea region, where increased Russian submarine activity has sparked concerns.
The Saber Guardian exercise rotates through Bulgaria, Romania and Ukraine, with a goal to increase the ability of European and U.S. military forces to operate together in the event of an armed conflict.
It will be the largest of 18 separate Black Sea exercises planned this year, European Command said.
The B-1B bombers were deployed from Ellsworth Air Force Base in South Dakota to a UK air base in Fairford to support two separate exercises planned this month, Saber Strike and BALTOPS, according to European Command.
Read alsoLatvia hosting NATO's Saber Strike drills (Photos, video)It said an undisclosed number of B-1B bombers would join three B-52H bombers that were already in Europe for training.
BALTOPS is a recurring multinational exercise that will involve 4,000 shipboard personnel, 50 ships and submarines and more than 50 aircraft.
Saber Strike, now in its seventh year, is aimed at improving cooperation among allies and partners while promoting regional stability and security, European Command said.