Mr Wright, who was elected to represent Texas's 6th congressional district in 2018, tested positive for Covid-19 in early January, following the Capitol riots.
At the time of his diagnosis, Mr Wright confirmed that he was experiencing "minor symptoms", but his campaign announced on Monday that he had died following his battle with Covid-19.
He died just one month after Louisiana congressman-elect Luke Letlow passed away following Covid-19 complications, and is the first sitting member of the House to die of coronavirus.
“Congressman Wright will be remembered as a constitutional conservative. He was a statesman, not an ideologue,” a statement released by Mr Wright's office on Monday read.
“Ron and Susan dedicated their lives to fighting for individual freedom, Texas values, and above all, the lives of the unborn," it added.
Mr Wright announced in July 2019 that he had been diagnosed with lung cancer, and was hospitalised in September 2020 with complications relating to his treatment.
His campaign said that despite his cancer diagnosis, Mr Wright "had kept a rigorous work schedule on the floor of the US House of Representatives and at home in Texas’ Congressional District 6".
He was a fixture in Texas politics, having served as Arlington mayor pro tempore between 2004 to 2008 and as the chief of staff to former representative Joe Barton between 2009 to 2011.
He later succeeded his former boss in the role as the representative for the 6th congressional district, when he was elected in 2018 and again in November 2020.
According to the Texas Tribune, Mr Wright is survived by his wife Susan, the couple's three children and nine grandchildren.
His campaign team said that his wife was by his side when he died, adding: "He is now in the presence of their Lord and Saviour."
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