Officials said Mohammed Abdulrahman Abu Niyan, a Saudi citizen, confessed to the murders which took place in the capital, Riyadh, earlier this month.
He received instructions, cash and weapons from IS elements in Syria, the interior ministry said in a statement.
Saudi Arabia is keenly aware that it is a key IS target, correspondents report.
IS has vowed to take over Saudi Arabia, the birthplace of Islam and site of its holiest mosques - and last year issued a call for followers to carry out attacks against Saudi targets.
Abu Niyan confessed to the 8 April attack on the police officers in a patrol car in the capital, the interior ministry said in its statement carried by state media.
The 23-year-old is also said to have admitted wounding two other policemen in a similar shooting in March.
According to officials, he carried out the attacks after contact with an IS representative in Riyadh.
The ministry said it was also offering a bounty of 1 million riyals ($270,000; Â£176,000) for the capture of an accomplice, Nawaf bin Sharif Samir al-Anzi.
The Sunni Muslim-dominated Saudi kingdom is part of a US-led coalition waging an air war against IS, which has seized swathes of Syria and Iraq.
Saudi Arabia says a man accused of shooting dead two policemen was acting on instructions from the Islamic State militant group.