About 350 of the skulls are believed to be from outside Sweden.
Talks between Te Papa and the institute to return the Maori skulls to New Zealand began in 2008, leading the institute to agree late last year to return them.
Sweden's Minister of Culture and Democracy, Alice Bah Kuhnke, said Government approval for the return of the skulls should be made this year.
Te Papa's repatriation manager Te Herekiekie Herewini said the museum was extremely proud of the relationship it has built with Swedish institutions to return Maori ancestral remains to their homeland.
"This relationship began in 1990 with a repatriation from the Ethnology Museum in Stockholm, and more recently with repatriations from two Gothenburg museums in 2009, and Lund University in 2011.
"We welcome reports that more ancestral remains will be returning home and look forward to receiving formal confirmation from the Swedish Government," he said.