The Russian space station has recently suffered a serious fire and a string of breakdowns in its life- support systems.
Via a radio link from the space shuttle Atlantis, Dr Foale was asked on BBC Radio 4's Today programme if he was worried that life on board Mir might be dangerous.
He said: "The most difficult thing we did, we did yesterday, and that was lift-off. That has by far the highest risk in it because you're going from zero miles per hour to 17,000 miles per hour.
"We've done that, we're in space, we're in orbit, and the rest of it is actually quite a lot easier."
Dr Foale, 40, originally from Louth, Lincolnshire, said the Atlantis crew expected to catch their first glimpse of the space station today. "We'll see it as a very bright star which will get steadily brighter and brighter."
He was looking forward to meeting two cosmonauts on board Mir with whom he had trained in Russia. Dr Foale will replace US astronaut Jerry Linenger, a naval captain and medical doctor, on board Mir.
During his mission, he will carry out scientific experiments, as well as help with repairs and maintenance of the space station. Atlantis is carrying a new oxygen generator and equipment to patch up a leak in Mir's cooling system.
Dr Foale, a Cambridge University postgraduate, has a doctorate in laboratory astrophysics. Pursuing a career in the US space programme, he moved to Houston, Texas to work on space shuttle navigational problems at the McDonnell Douglas Aircraft Corporation.
In June 1983 he joined NASA's Johnson Space Center, working in payload operations. He was selected for astronaut training by NASA in June 1987 and is a veteran of three space flights.
In November 1995 he flew on the first shuttle to rendezvous with Mir. During the flight he made a four-hour-and-39-minute space walk to test the effect of extreme cold on his space suit.Reuse content