He described himself as an “unapologetic unionist who will always advocate confidently for Northern Ireland’s place in the United Kingdom”.
Under his leadership, Burrows said the UUP will be “clear, credible and on the front foot”.
He said his priorities would be competence and delivery, cutting waste, economic growth, and better public services.
Burrows also said he would seek to attract more women and young people to the UUP.
“One female MLA out of nine is not good enough. I will address these issues with urgency”, he said.
Formal nominations opened on Wednesday and will close on 15 January.
As part of this process, the party will also host two internal, members-only, hustings events to allow prospective candidates to engage directly with the membership.
There has also been speculation that the current deputy leader, Robbie Butler, who is from the liberal wing of the party will stand for the leadership.
BBC News NI understands that both Burrows and Butler approached Diana Armstrong to be their running mate.
Her constituency represents a large swathe of grassroots UUP voters who will have a say in any contest.
Armstrong refused to comment on those discussions but said she had backed Burrows because he is a man of integrity and that the party needed “fresh thinking”.