As bishop in Europe, Browning had jurisdiction over Episcopal churches in Germany, Switzerland, Belgium, Italy and France.

Browning oversaw the closing of the Episcopal Church of the Holy Spirit in Nice, in connection with the withdrawal of U.S. forces from France.

In 1976, he was elected Bishop of Hawaii and was installed at the Cathedral Church of Saint Andrew, Honolulu on August 1 of that year.

On September 19, 1985, Browning was elected to succeed the Most Reverend John Maury Allin as Presiding Bishop at the General Convention held in Anaheim, California.

I think the Church has a role in being both prophetic in holding up issues, and using all its influences to try to bring about better conditions for the poor, the hungry, both in this country as well as in the global village.

In his sermon, he began to address the deepening rift within the church over issues such as the ordination of women and homosexuality, by saying: "(Do not ask me) to honor one set of views and disregard the other.

Browning also supported the adoption of a pro-choice stance on abortion by the Episcopal Church at their 71st General Convention in 1994, the first taken by an Anglican Communion province.

[6] The last year of Browning's term was shadowed by a financial scandal when it was revealed in May 1995, that Ellen F. Cooke, the former treasurer of the ECUSA, had diverted $2.2 million to her own use.

[7] Cooke was national treasurer from her appointment by Browning in 1988 until he forced her to resign in January 1995 due to her abrasive management style.

Browning admitted that Cooke's embezzlement had gone undetected because she had "absolute control over auditing" and had prevented any outside checking of accounts.