Relations between Russia and the West have plunged over the Ukraine conflict.
Mr Stoltenberg described the new unit as a "big step forward toward greater solidarity... greater readiness".
He joined Lithuanian President Dalia Grybauskaite for the opening ceremony in Vilnius on Thursday.
President Grybauskaite welcomed the new units in the region, saying they would ensure the "quick and effective" movement of troops.
The six so-called Nato force integration units (NFIU) are intended to enable the speedy deployment of Nato`s rapid reaction forces at a time of crisis, reports the BBC`s diplomatic correspondent Jonathan Marcus.
Typically they will be some 45-50 strong made up of local and international military personnel, our correspondents adds.
They will make practical arrangements for deployments - such as identifying fuel supplies and suitable bases.
The aim is to have all six units fully capable by Nato`s Warsaw summit in the autumn of 2017.
Bulgaria, Estonia, Latvia, Lithuania, Poland and Romania - all former communist states - joined Nato and the EU in 2004.
Both bodies accuse Russia of directly helping separatists in eastern Ukraine with regular troops and heavy weapons. Russia denies the claims.
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