The son of songwriter Fred Rose, he was born in Chicago, Illinois, and studied to become a Chartered Accountant. He eventually moved to Nashville, Tennessee where in 1945 he became involved in Acuff-Rose Music, a music publishing house established by his father and his father's partner, Roy Acuff. Following his father's death in 1954, Wesley Rose served as the company's president. He proved to be a very capable businessman, expanding the business significantly and establishing Acuff-Rose affiliate offices around the world.
Wesley Rose was a very important part of the development of the country music industry. He was a driving force behind the creation of the Country Music Association (CMA) and was the first Nashville publisher to serve on the Board of Directors of the American Society of Composers, Authors, and Publishers (ASCAP) and the Music Publishers Association.
Wesley Rose died in Nashville in 1990.