The man also admitted to carrying out a separate attack on a bus carrying foreign workers on Monday.
"A man accused of opening fire on the workers was arrested. He confessed to carrying out the attacks against the Americans yesterday," a state-run Kuwait Television broadcast announced.
The attack on Monday left five Asian and Egyptian workers wounded, when bus came under fire south of Kuwait City close to an area where US troops operate.
Four US soldiers were slightly injured in Sunday's shootings on their convoys, according to a US army spokesman.
A security source, quoted by the official KUNA news agency, said the main suspect is a Kuwaiti national. Three accomplices are also under interrogation to establish if they were involved in the shootings, he added.
Monday's shooting on the bus and Sunday's second attack on a US army convoy took place near the oil and industrial area of Shuaiba, 50 kilometers (30 miles) south of Kuwait City.
US troops operate almost exclusively in the area's port, which is Kuwait's second commercial terminal, to unload arms, weapons and equipment for the US army in Kuwait and Iraq.
A statement by the US embassy in Kuwait on Monday said the shooting incidents were believed to be terrorist attacks.
Kuwait served as a launch pad for last March's US-led invasion of Iraq which led to the ousting of Iraqi president Saddam Hussein, who was captured on Saturday after eight months on the run.
Thousands of US troops are based in Kuwait, which is also being used as a transit point for American soldiers going home on vacation or returning to their bases in Iraq.
The string of attacks came ahead of a summit of the Gulf Cooperation Council (GCC) in Kuwait, during which cooperation in combating terrorism among the six-nation alliance is expected to top the agenda.
Kuwait stepped up security after intercepting on Friday three letter bombs sent to journalists and a small explosion at a
newspaper the previous day.
Security measures had already been heightened in preparation for the GCC summit and the Gulf Cup soccer tournament from December 24 to January 11.