The 30-year-old Nelsen, chosen as one of New Zealand's three allowed over-age players in the under 23 competition, will be available for the first two matches against hosts China on 7 August and Brazil on 10 August.
Nelsen will miss the final pool match against Belgium on 13 August to return to England to prepare for Blackburn's opening Premier League match of the season against Everton.
New Zealand coach Stu Jacobs said the decision by new Blackburn manager Paul Ince to release Nelsen was a "terrific outcome".
He said Nelsen was delighted he could play for his country and realised how important it was for New Zealand to take its best team to the Olympics. "I think all the way through the process, he has been pretty desperate to be part of it."
Nelsen will join Glasgow Celtic striker Chris Killen and former Fulham midfielder Simon Elliott as the three permitted over-age players in the team.
The full New Zealand squad is due to be named on Thursday.