In a message published on the Vanilla Black website, the pair said that as a direct result of the Coronavirus crisis they were unable to see a financially viable way to reopen the restaurant.
"As a small independent restaurant which has traded for 16 years, the effects of the last few months have been immensely devastating," they wrote.
"We have always put our hearts and souls into Vanilla Black and it is a passion rather than a business, so it has been a very difficult decision to make."
Dargue and Conroy originally opened Vanilla Black in York in 2004, and subsequently relocated the restaurant to London in 2008.
The restaurant, which was recommended in the Michelin Guide, was heralded for its innovative approach to both vegetarian and vegan cuisine.
Paying tribute to the restaurant on Twitter, Restaurant columnist Tony Naylor wrote: "If you know, you know etc. [Vanilla Black] was an outlying envelope-pusher back when the idea of ambitious, creative vegetarian cooking was still seen as an amusing novelty.
Despite the sadness of having to close the doors of their Holborn site, Dargue and Conroy say this is not the end for them.
"This is never the way we imagined it," they added.
"This is not the end of our mission to create innovative vegetarian and vegan cuisine.
"We will return in the near future with a new and exciting venture."