Peterson said he hoped the deal would also make the NZX more attractive for prospective new listings.
He said the Nasdaq was also keen to use the NZX to test new innovation as a beta site.
"The Nasdaq is really keen to work with us," he said.
NZX already has a close technology relationship with Nasdaq, operating its trading and surveillance systems since 2012.
Peterson said it began talks with the US exchange at the end of last year and it had taken a little bit of time to do the deal.
"It's not a five-minute thing, we want it to be a long-lasting relationship," he said.
The memorandum of understanding enables issuers listed on the Nasdaq's top-tier equity board, the Global Select Market, to apply for a secondary listing on the NZX under the foreign exempt issuer regime.
Under this regime, issuers comply with the primary rules of their home exchange, and are exempt from almost all NZX listing rules.
NZX chairman James Miller said the Nasdaq MOU complemented relationships it had already with the Singapore and Hong Kong exchanges.
"We look forward to working with Nasdaq to generate opportunities for investors and companies in our respective markets."
A visit from top Nasdaq executives is expected to further the discussions.