The cease-fire is set to take effect July 9 at noon Damascus time.
The deal is separate from an agreement that Russia, Turkey and Iran struck earlier this year to try to establish "de-escalation zones" in Syria with reduced bloodshed.
The remarks offer the latest stop on a bumpy USA policy ride that has left global observers with a case of diplomatic whiplash as they try to figure out whether the Trump administration will insist that Assad step down from power.
Both oppose the Islamic State group in Syria.
And by flexing their military reach in Syria with a missile launch, Iran's Revolutionary Guards and other regime hardliners risk inflaming more tension with the Trump administration - tension that could boil over in the coming war for dominance of southern Syria.
Israeli daily Haaretz reported on Thursday that Israel told the US that it doesn't want Russia supervising proposed safe zones in Syria during ongoing talks being conducted between the US, Russia and Jordan.
It also came as US-backed fighters inched forwards in Raqqa's Old City, in what Washington sees as a milestone in the campaign to defeat the Islamic State group in its de facto Syrian capital.
For years, the US and Russian Federation have been backing opposing sides in Syria's war, with Moscow supporting Syrian President Bashar Assad and Washington supporting rebels who have been fighting Assad.
Randa Slim, director of The Middle East Institute's Track II Dialogues initiative, which looks at facilitating policy and problem solving in the region, said Mr Tillerson's statement and the ceasefire announcement "define the negotiation framework for US-Russia coordination in Syria".
Tillerson said the difference this time is Russia's interest in seeing Syria return to stability.
Tillerson also said Russian Federation had an obligation to prevent the use of chemical weapons by Assad regime. How he leaves could be determined later, the political process should include a transition away from the Assad family, he added. It was reported last month that Mr McGurk and US Syria envoy Michael Ratney held secret talks with Russian Federation in Jordan in May.
The Syrian war broke out in 2011 when Assad's government cracked down on antigovernment demonstrations.