Brennan was selected by the Browns with the 104th overall pick in the 1984 NFL Draft and spent the first eight seasons of his nine-year career in Cleveland. In 1986, Brennan helped lead the Browns to a 12-4 record, where he finished the season with 55 receptions for 838 receiving yards and six touchdowns. Amongst Browns all-time career leaders, Brennan's 315 receptions rank fifth, his 4,148 receiving yards rank ninth and his 19 receiving touchdowns are tied for the 15th most.