Clean, by Sabrina Mahfouz, and A Respectable Widow Takes to Vulgarity by Douglas Maxwell, were performed at the Oran Mor venue in Glasgow's west end last year, after first being shown at the Fringe in 2012.
Now they are to be staged at a leading off-Broadway venue in New York - 59E59 Theaters.
Both works were first produced by the Traverse Theatre as part of its Dream Plays in 2012, which won a prestigious Herald Angel award, and were recently re-staged at the Traverse.
In Clean, three "no nonsense criminal heroines" take part in a heist, while in Maxwell's play a mourning widow strikes up an unlikely relationship with her husband's foul-mouthed employee.
Bella Loudon, the assistant director of the plays, staged at Oran Mor last February and March, said: "It's very exciting, and of course it is a very new audience for the plays and it will be interesting to see how they go down.
"It is a very significant opportunity for the cast and the writers."
The plays, both directed by Orla O'Loughlin, run at the New York venue from April 2 to April 27, and are being presented as a double bill, with a total running time of under two hours.
This is the Traverse Theatre Company's third transfer to New York in recent years, following David Harrower's Good With People in March 2013, and David Greig's Midsummer in January 2013.
Linda Crooks, executive producer of Traverse, said: "Our invitation to 59E59 Theaters for the second year running is a testament to the quality of work Traverse Theatre Company produces year on year.
"With an international reputation for discovering and producing high calibre new writing talent, it is an honour to present our work to the New York audience."
Mr Maxwell said: "Ever since it was part of Dream Plays, A Respectable Widow Takes to Vulgarity has surprised me constantly in the way it has been so well received.
"After proving so successful with Scottish audiences, it's a real joy to see it head to New York. It'll be a wee joy to see how Joanna Tope delivering brilliantly strong language goes down with an American audience."
Ms Mahfouz said: "The cast of Clean have a wonderful way of delivering the words that originated as a 48-hour challenge back in 2012. I can't wait to see them in action again.
"Clean going to New York is such a dream. I love the energy of the city and I plan to see as many plays as I can while I'm there."
The venue, which is owned and operated by the not-for-profit Elysabeth Kleinhans Theatrical Foundation, is on 59th Street between Park and Madison Avenues in Manhattan.
The plays are part of the Brits Off Broadway season, an annual festival of writing from the UK.
Ms Crooks added:"[Both plays] have a strong team behind each production, including Orla O'Loughlin, and assistant directors Bella Loudon in Scotland and Emily Reutlinger in New York."