It will be the first rugby league fixture at the 54,000-capacity venue.
Hull's KC Stadium will kick off the series on Sunday, 1 November, while Wigan's DW Stadium stages the final Test on Saturday, 14 November.
New Zealand beat England in the 2013 World Cup semi-final at Wembley on their last visit to London.
"The Olympic Stadium provided the backdrop to some truly most memorable action at London 2012 and it is simply fantastic that we have reached an agreement for England to play New Zealand there in November," said Rugby Football League chief executive Nigel Wood.
"The Kiwis are our oldest rivals on the international stage and the match at Olympic Stadium will provide one of the highlights of a historic year for the sport as we celebrate our 120-year anniversary in 2015."
Steve McNamara's side were narrowly beaten in last Autumn's Four Nations series by the eventual winners New Zealand and Australia, who have opted for 2015 as a rest year.
"The fans should be excited about the England team, the way they have played against us and Australia recently, they have been great contests," said New Zealand coach Stephen Kearney.
"I think they were unlucky to lose in Melbourne. The fans should be proud of their team, hopefully they will fill the Olympic Stadium and make it a great occasion."
Since the closing ceremony of a successful 2012 London Olympics and Paralympics in September of that year, the venue has been secured for a number of sporting events.
Premier League side West Ham United won the bid to seal tenancy of the stadium from August 2016, following a conversion of the venue.
Rugby union will also make its debut appearance at the stadium in August when the Barbarians play Samoa on 29 August, as a precursor to its host venue status in the World Cup.
The London Athletics Grand Prix was staged on site, while concerts have been held outside the stadium in its grounds.
England will play one of their three-match Test series games against New Zealand in the Olympic Stadium in London on Saturday, 7 November.