Here is his statement in full.
Shortly before the election campaign, I made the decision, in the event that Labour was defeated and a new leader was to be elected, to stand for the leadership of the party if there was a desire in the party for me to do so.
I dearly hoped Labour would win the election and it was a decision I would not have to implement.
I also thought I understood the scrutiny and attention a leadership contest would bring.
As a member of the Shadow Cabinet, I am used to a level of attention which is part and parcel of the job. I witnessed the 2010 leadership election process close up and thought I would be comfortable with what it involved.
However, since the night of our defeat last week I have been subject to the added level of pressure that comes with being a leadership candidate.
I have not found it to be a comfortable experience.
One can imagine what running for leader can be like, understand its demands and the attention but nothing compares to actually doing it and the impact on the rest of one's life.
Consequently after further reflection I am withdrawing my candidacy.
I apologise to all those who have kindly supported and encouraged me to do this and for disappointing them.
I know this will come as a surprise to many but I had always wondered whether it was all too soon for me to launch this leadership bid - I fear it was.
Most importantly, I continued to have very real concerns and worry about this bid's impact on those close to me.
I intend to carry on playing my full role as a proud member of our Shadow Cabinet taking on the Tories.
I also hope to play a leading role in Labour's campaign to keep the UK in the EU during the forthcoming referendum which is absolutely crucial.
Most importantly, I will as ever continue to serve the area I know and love - the Streatham parliamentary constituency.
Shadow business secretary Chuka Umunna has withdrawn from the Labour party leadership contest citing the uncomfortable pressure of extra scrutiny on his life.