Gregory, who takes up the role with immediate effect, will be oversee the day-to-day running and direction of the company, which offers free calls and SMS messaging to consumers willing to be targeted with advertising on their phones.
Blyk, which went live at the end of last month, was founded by Pekka Ala-Pietila and Antti Ohrling.
Gregory said: "Blyk has one of the most compelling advertising opportunities I have ever seen. It can reach, engage and build relationships with consumers on a very personal level. It's also focused on the youth market which is notoriously difficult to reach."
Gregory joined the Telegraph last October, and was charged with expanding its online, TV and mobile operations. Before that he was a senior executive at Emap Radio.