The announcement was made today (Thursday) during the Queen's Platinum Jubilee celebrations.
Mr Wright has previously held the positions of attorney general and culture secretary, before leaving government when Boris Johnson entered Downing Street.
Mr Wright said: "I feel hugely privileged and grateful to be included in Her Majesty the Queen’s Birthday Honours List, especially in this Platinum Jubilee year and in such remarkable company.
"The work in Government for which I am being recognised was made possible by the effort and ingenuity of many colleagues in the departments in which I worked as a Minister, as well as by the confidence of the constituents I have had the honour of representing for the last 17 years.
"I want to thank them all. I also want to thank my family, staff, friends and many others, without whose love and support I could not have done any of it."