The move is aimed at deterring potential Russian aggression on NATO's eastern flank, where tensions have mounted since Russia's invasion of Ukraine in 2022.
"The German armed forces are ready to become a central pillar of conventional deterrence and defence in Europe," Pistorius told lawmakers in the Lithuanian capital of Vilnius.
Germany has committed to permanently stationing 5,000 troops in Lithuania by the end of 2027, a decision Berlin considers pivotal to its defence policy. Pistorius vowed to respect the deadline.
"This is in our shared interest. And it is our shared responsibility to make this flagship project a success," the minister said.
"Bearing in mind the terrible experience Lithuanians had to go through with Nazi Germany in the first half of the last century this friendship means a lot to me personally and to the German people," he added.
Several hundred German troops are already in Lithuania and around 500 personnel expected next year.
Lithuania has committed to building infrastructure for the German brigade and is ratifying a bilateral agreement that outlines the rights of German troops stationed in the country.
The treaty, which is expected to pass next week, will permit Germany to establish educational institutions, mess halls, and military shops in Lithuania, all of which will be exempt from taxes.
Additionally, Lithuania will ensure access to healthcare services for German troops and civilians, while the German military reserves the right to "establish health care, dental, and veterinary facilities" as required.
Pistorius said Germany would ratify the agreement next year.