Kiley's job, which was the outcome of an agreement with the government, gives him a direct role within the PPP and puts him in charge of negotiations with bidders. Livingstone said this would avoid the need for the Greater London Authority to take the government to a judicial review, scheduled for 16 June.
He told Building: "I am confident that Kiley can ring the changes needed to the PPP contracts to make them safe by then." Under the agreement, Kiley will be given the chance to put the Tube under more centralised control without breaking with the financial constraints of the PPP deals.
He was due to begin detailed negotiations with the preferred bidders on Wednesday.
Livingstone also expressed more confidence than hitherto in the two preferred bidders picked for Tube line last week.
Last year, he described them as the "worst scum of modern capitalism"; now he conceded that they could do the work, "provided they are not had up for corporate manslaughter".
The government selected the Tube Lines consortium, (Bechtel, Amey and Jarvis) for the Jubilee, Northern and Piccadilly lines. Metronet (Balfour Beatty and WS Atkins) won the Bakerloo, Victoria and Central lines.
A spokesperson for Tube Lines said the consortium welcomed the chance to talk to Kiley.
She said: "We are glad of the opportunity to show exactly what we have got on the table. It looks like it's going to be sooner than we first thought." A Metronet spokesperson said the consortium was awaiting the further details that would emerge from its discussions with Kiley.
A source close to one bidder did express concern at the new understanding between Kiley and the government. The source said: "It's confusing and disappointing. We want to get on with this but this will delay the financial close of the deal even longer." Speaking before the Kiley agreement was announced, Tube Lines chief executive Iain Coucher said he was confident that any differences over the deal could be ironed out.
"All the partners want to improve the Underground. All the people involved have the integrity to work to make this better." Coucher defended the structure of the deal against concerns over management control and safety.
He said: "They [London Underground] have absolute control over what we do. They haven't got control over how we do it. This is quite clear.
"To suggest that having different parties is unsafe is misleading. As long as there is clear responsibility and accountability over who does what, there is not a problem." Coucher claimed that the detail of the bids, which has also come under fire from Kiley, was exhaustive.
He said: "We had 100 engineers working for 18 months on this. We were not asked for full details by London Underground. When we submitted the bids, it was in 14 boxes. If we had supplied all the detail we had, it would have been more like 114 boxes." Coucher said the consortium was aiming to add 300 staff to London Underground's workforce once the deal was signed.