His predecessor, Dame Helena Shovelton, resigned after a High Court ruling overturned her decision to negotiate the next seven-year lottery operating licence only with Richard Branson's People's Lottery and not with Camelot.
Culture Secretary Chris Smith, who appointed Lord Burns, said: "Terry Burns has a most distinguished record and I am delighted to appoint him to the Commission".
The government will now hope that his appointment will bring credibility to the selection process for the next lottery operator.
The court ruling said the commission had acted unfairly and ordered it to restart negotiations with Camelot.
Challenging job
On appointing him, Mr Smith wrote to Lord Burns explaining that he realised the former Treasury permanent secretary was taking over the job at a "particularly challenging time".
"I wish to give you a clear remit, with the other commissioners, to conduct the selection process with absolute fairness and impartiality between the applicants. There can and will be no ministerial or political interference," Mr Smith wrote.
And Mr Smith reiterated his determination that there should be no interruption in the running of the Lottery no matter who won the contract to run it.
He told Lord Burns: "I look to you to take all necessary steps to achieve this."
Lord Burns indicated at a photocall in central London that he was the aware that the job posed difficulties.
He said: "It is clearly not an easy job, but I believe it can be done otherwise I wouldn't have taken it on."
Controversy
Camelot welcomed Dame Helena's resignation at the time as a "step in the right direction" to ensure fair competition.
But in an interview recorded for the BBC programme Watchdog, Sir Richard Branson accused Camelot of conducting a "below the belt" smear campaign aimed at derailing the bidding process
In the past, Mr Smith has been a strong critic of the high profits made by Camelot and the high salaries paid to its directors, and has called for a non-profit lottery.
Lord Burns refused to be drawn on the issue saying: "I can't comment on what has happened in the past. The important thing is to look forward."
But he will have to move fast, the Commission has promised to reach a decision as soon as possible - probably in early in November.
The part-time job of lottery commission chairman comes with an annual salary of £48,000 and a three-year tenure.