The Nato force integration unit in Lithuania is one of six new centres also located in Bulgaria, Estonia, Latvia, Poland and Romania.
Relations between Russia and the West have soured 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.
Poland joined Nato in 1999, then in 2004 Bulgaria, Estonia, Latvia, Lithuania and Romania also joined. All six were formerly in the communist bloc. They became EU members in 2004.
Both bodies accuse Russia of directly helping separatists in eastern Ukraine with regular troops and heavy weapons. Russia denies the claims.
Nato Secretary General Jens Stoltenberg has inaugurated one of the alliance's new command units opening in Eastern Europe amid tensions with Russia.