The mosque is located at University of Malaya in Jalan Pantai Baharu and was named after the first Malaysian Prime Minister, Tunku Abdul Rahman Putra Al-Haj.

Today, the mosque is joint managed by University of Malaya and the Department of Federal Territory Islamic Affairs (JAWI).

The foundation stone of the mosque was laid down by the first Malaysian Prime Minister, Almarhum Tunku Abdul Rahman Putra Al-Haj on 6 November 1962.

On 23 August 1963, the mosque was officially opened by the third Yang di-Pertuan Agong, Almarhum Tuanku Syed Putra Jamalullail of Perlis.

In 2010, the mosque started hosting a methadone programme combined with praying to treat drug addicts.