Swire returns to the backbenches, having served as Minister of State at the Foreign and Commonwealth Office since 2012, Express and Echo reported.
The former Minister for Northern Ireland in the coalition Government was a close ally of David Cameron.
But he will not be serving under new Foreign Secretary Boris Johnson after the new Prime Minister finalised her cabinet and ministerial team over the weekend.
Mrs May did not find a role for Swire, despite him backing her for the Tory leadership and having previously served as her Parliamentary Private Secretary when she was chairman of the Conservative Party.
Swire, who has represented East Devon in Parliament since 2001, tweeted: “I am retiring to the backbenches to join my friends.
“It’s been an honour and a privilege to have served as a Minister in the Government since 2010.”
Plaudits for his time in office came from, among others, British Ambassador to Chile Fiona Clouder, who replied: “Thank you for all you have done to further relations with Latin America, including Chile. Important for the future.”
Simon McDonald, Permanent Under-Secretary at the FCO, tweeted: “On behalf of @foreignoffice I thank Hugo Swire for energetic, imaginative & effective service.”
The former Japanese ambassador to the UK Keiichi Hayashi tweeted: “Many thanks for six years’ dedication as minister covering vast area including Japan and personally for your friendship. Wish you v best.” (Colombo Gazette)