The broadcaster returned to the early morning show in November after weeks away ill.
He told the Daily Mirror: "It was nothing life-threatening. I had a couple of complications with my vision. They sorted it out very quickly and I was in fantastic hands in the NHS. It was really easily treated in the end."
Turnbull said he had "a quick look" at ITV's new rival show Good Morning Britain, which is presented by his former BBC colleague Susanna Reid.
The pair shared the sofa on BBC Breakfast for years before Reid jumped ship, but 58-year-old Turnbull said he had signed up to present the show for two more years.
He said: "We have heard from a lot of people who say they have looked at the other side and they want to stick with us and that is what I am pleased about."
His BBC show has regularly outperformed its ITV rival in the ratings, but earlier this week ITV boss Peter Fincham said the channel was "right behind" Good Morning Britain.
Mr Fincham told the Broadcasting Press Guild the show was "fresh" and "different".
He said: "This is two or three weeks into the life of Good Morning Britain. In the life of a breakfast show that is a nanosecond, so it's very early days and we're fully right behind it."
Reid, who quit the corporation to join the weekday show, works with co-hosts Ben Shephard, Charlotte Hawkins and Sean Fletcher, but Mr Fincham denied viewers were put off by reports of large salaries for the show's stars.
He said: "There are plenty of presenters on all mainstream channels that are very popular with audiences and are very well-paid. That's the nature of television."