The agreement to clean the area was reached at a meeting between the US department of energy and Spain's CIEMAT, the national center for energy and environment investigation, the Spanish daily newspaper, El Pais, reported on Sunday.
The agreement states that the countries will jointly pay for the costs of the clean up that could take years to complete depending on the levels of radioactivity found, the article said.
"Not even the Americans know what is there. There could be nothing, but there could be a problem and if there is, it will be solved," Juan Antonio Rubio, CIEMAT's general director, said in the article.
The accident took place on January 17, 1966, when a B-52 bomber collided with a flying tanker - while refuelling over Palomeras, in Southern Spain - releasing all four of its hydrogen bombs in the ensuing explosion.
The high-explosive igniters on two bombs detonated on impact, spreading radioactive material, including plutonium, over a wide area of the Spanish countryside.
A third bomb landed relatively intact and was recovered.
The fourth bomb landed in the Mediterranean Sea, and US military searchers took months to find and recover the device.
Seven of the 11 crewmen aboard the two planes were killed in the collision. There were no fatalities on the ground.