Wilson joined the Rupert Murdoch-owned tabloid in 2007 and has covered politics for other newspapers since 1997.
He replaces Susie Squire, who is leaving to join her husband in South Africa.
Squire has been in the role for less than a year, having taken over when David Cameron's longstanding press secretary Gabby Bertin went on maternity leave in November 2012.
Bertin is returning as director of external relations this autumn. She started working as Cameron's press secretary in 2007 and retained the role at Number 10 when he entered government.
David Wooding, associate political editor of The Sun, said Wilson would be an asset at Number 10 because of his ‘great news judgement’.
‘He is liked and respected by all the journalists, and people will trust him because he is plain-speaking and honest and straight as they come.’
He added that the hire would help the Downing Street operation as it ‘changed emphasis’ looking ahead to the elections.
‘Everything is going to start being geared in that direction, with new ideas for the onslaught on the other parties required. Having someone new, and someone who knows a great story and how to present it, to take on that emphasis will be good for them.’