Tory Party members are voting for either Mr Johnson or Foreign Secretary Jeremy Hunt to succeed Theresa May as their new leader. The winner is expected to be announced on Tuesday, July 23.
Mr Asghar said: “I have received dozens of emails, letters and phone calls and have spoken face-to-face to many constituents on this issue.
“By a clear majority they have said Boris Johnson is the best person to unite our country, deliver Brexit and secure the brighter future we all wish to see.”
Mr Asghar, who used to represent Plaid Cymru in the Senedd, thanked constituents who had contacted him. He had previously said he wanted to give constituents, who were not members of the Tory Party, a chance to select the next Prime Minister through his vote.