The former managing director of Emap Metro was working as a part-time consultant with Emap last year and contributing to a number of titles including The Observer, The Word, and Radio Times.
In 2004, Mcllheney headed up the launch of Zoo in the UK and then went on to help launch the title in Australia and South Africa.
Prior to this, Mcllheney led the launch of several of Emap's magazines, including Heat, FHM (in France) and Empire magazine, which he edited for three years. The title became the UK's biggest-selling movie magazine.
Andrew Fickling, executive director of Sport Media Group, said: "Barry has a proven track record of creating significant circulation uplift, particularly in the men's publishing arena.
"As just a small increase in the circulation of the Daily Sport and Sunday Sport can deliver a significant increase in group profits, this appointment is critical to the continued success of the business."
Mcllheney also edited Smash Hits magazine back in the 1980s when it became the world's biggest-selling music magazine.
He said: "With the success of men's monthly and weekly magazines, it is only a matter of time before we have the first men's daily. As the rest of the newspaper market increasingly target women and older readers, this is real chance to produce a modern British tabloid for modern British blokes.
"Any man interested in sport, women, and having a laugh -- and in my experience there are quite a few of them -- now at last has a national daily newspaper he can be proud of."