The move comes amid continued tensions between Christians and Muslims in the Southeast Asian nation.
"I am delighted by the appointment of Archbishop Joseph Marino as the first Apostolic Nuncio to Malaysia," Najib said in a statement.
"Having established diplomatic ties in 2011, Pope Benedict XVI and I vowed to work together to increase understanding between Christians and Muslims. The appointment is a testament to this commitment."
The American archbishop will also serve as an envoy to Malaysia's smaller neighbours East Timor and Brunei, according to a report on the website of the Vatican Insider.
The Vatican and Malaysia established official diplomatic ties after Najib visited the Holy See in July 2011.
The visit came after he met with Malaysian church leaders in a bid to ease religious tensions stirred by a report that alleged Christians wanted to replace Islam as the official religion in the country.
The row is one of a string of religious disputes in recent years that have raised fears among minorities of a growing "Islamisation" of Malaysia.
Several places of worship were attacked in 2010 after the High Court lifted a government ban on non-Muslims using "Allah" when translating "God" into the Malay language.
The government strongly criticised the attacks, but tensions over the issue have continued to simmer.
Religion and language are sensitive issues in multi-racial Malaysia.
More than 60 percent of Malaysia's 29 million people are Muslim ethnic Malays, but it also has sizeable Chinese and Indian minorities. Nine percent of the population are Christians, including 850,000 Catholics.