The couple will welcome their child in the fall.
Varela's rep told People: "It's Leonor's first child and the couple are over the moon."
The actress can be seen on TNT's reboot of the iconic series Dallas as Marta Del Sol.
Her previous credits include Blade II, The Tailor of Panama and Arrested Development.
Dallas premiered last month in the US and was immediately renewed for a second season by TNT.
The show will debut on Channel 5 in the UK later this year.
Akoskin is currently producing Words with Gods and previously starred on the 2007 comedy The Doorman, which he also produced and wrote the screenplay.
Watch the trailer for Dallas below: