"It's our duty to the state, my duty as outgoing president (to help the president-elect)," she said after meeting with Nauseda at the Presidential Palace.
Grybauskaite said Nauseda and she found "a lot of common perception and understanding about the state".
The outgoing leader expects that "the huge confidence that people have placed in the president-elect will be justified".
"This is both confidence and great responsibility," she said.
Nauseda said they shared views on topical issues and the outgoing president informed him about the forthcoming tasks.
"I can see a deep wish to make (...) that (transition) process as smooth as possible, based on mutual understanding, mutual respect," he said.
The outgoing and incoming presidents made brief statements to the press after their meeting but did not answer journalists' questions.
Nauseda, who was elected president in Sunday's runoff against Ingrida Simonyte, will take office after his inauguration ceremony in July.