It features the Welsh dragon, the English lion, the Scottish unicorn and a stag for Northern Ireland.
Rt Rev Gregory Cameron has also been able to incorporate his initials.
The final batch of round £1 coins for public circulation were struck at the mint in Llantrisant, Rhondda Cynon Taff, in December.
A new 12-sided £1 coin, billed by the Royal Mint as the "most secure coin in the world", is to be introduced in 2017.
Rt Rev Cameron, an amateur artist and coin collector, said: "I am absolutely delighted and proud that I have designed the very last commemorative round pound coin.
"In my design, the four heraldic beasts are equal - each has its quarter of the coin.
"There is also some cross-over - parts of each beast cross over into the next. That makes it more dynamic and also symbolic as it shows four separate nations, all an equal part, yet interlinked as they protect Britain's sovereignty, the Crown.
"As a Welshman, I put my initials GKC under the dragon."
Royal Mint commemorative coins director Anne Jessopp said the commemorative "farewell" pound was all the more special, given it was the last.

The ICC Development Programme Annual Awards have been running since 2002 and are open to countries who are associate and affiliate members.
Cricket Scotland's Ian Sandbrook said: "This is great recognition for our clubs, schools, coaches, volunteers and staff that have all put in a huge amount of effort to grow and sustain the game we love."
The winner of the ICC award receives a cricket equipment grant of £3,500 to its national cricket body.
Cricket Scotland's head of participation was delighted to receive such recognition for its grassroots programmes.
"We are continually looking at how we can improve our work with clubs, schools and other key stakeholders to attract new people to the game and build a sustainable future for cricket," said Sandbrook.
"Great initiatives like the Thriving Clubs Programme, CricketForce, Community Coaching Programme, our new Club Awards, Last Man Stands leagues, the roll out of the curriculum for excellence programme, and our continued growth in female cricket, has started to establish a stronger foundation for the game to flourish.
"From my perspective, we have only just started and we're absolutely committed to building on this to take cricket to the next level in Scotland."
Meanwhile, Scotland will play two one-day internationals against Afghanistan at The Grange in Edinburgh on 4 and 6 July, with Hong Kong visiting the same venue on 8 and 10 September.
A final commemorative round £1 coin has been struck using a design created by the Bishop of St Asaph following a Royal Mint competition.
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Scotland has won the International Cricket Council's Best Overall Cricket Development Programme Award for 2015.