The poll, commissioned for the Evening Standard newspaper, suggests Mr Johnson has the support of 51% while Mr Livingstone is the preferred choice of 49%.
Last week the polling company placed Johnson 6 points ahead of Livingstone, slightly down on an earlier 8 point lead.
Mr Livingstone had started the year with a 2 point lead over Johnson however a series of headlines about his tax affairs helped push his rival back into the lead.
However in recent weeks Livingstone has attempted to steer the headlines “back towards the issues” and focussed much of his efforts on highlighting his promised 7% fares cut.
Today’s poll suggests the result of next week’s election is now too close to call.
When voting for Mayor, Londoners are able to cast one vote for their first preference candidate and one vote for their second preference.
If no candidate secures more than 50% of the first preference votes, the two highest scoring candidates go through to a second round and all second preference votes allocated to the candidate they were cast for.
The candidate with the highest number of first and second preference votes is then elected Mayor.
On first preference votes Johnson has 43%, Livingstone 41%, Liberal Democrat Brian Paddick 8%, UKIP’s Lawrence Webb and independent Siobhan tie on 3% and Green party candidate Jenny Jones 2%.
After the reallocation of 2nd preference votes, front runners Livingstone and Johnson remain just 2% apart.
YouGov also polled Londoners on their voting intention in the London Assembly elections.
14 Assembly Members are elected to represent constituencies under the First Past the Post system used to elect MPs.
A further 11 are elected under a proportional representation (PR) list which ensures all parties with 5% of the vote win seats.
According to the poll, Labour are 12 points ahead in the constituency vote with 46% of the vote while the Conservatives have 34% and the Liberal Democrats 9%.
In the list section Labour remain ahead with 44%, the Conservatives have 33% and the Liberal Democrats 9%.
The poll puts the Greens on 6% suggesting they will keep at least one of the two seats they currently hold while UKIP, who won seats in 2004, look set for a return to the Assembly with 5% of the vote.
Candidates for Mayor include Jenny Jones (Green party), Ken Livingstone (Labour), Lawrence Webb (UKIP) Boris Johnson (Conservative) and Brian Paddick (Liberal Democrat). A full list of candidates can be found here.