Bishop Joanna Penberthy, who was elected Bishop of St Davids last year, gave the address at the service on Sunday morning.
The theme of the service was Citizens of the World and Bishop Joanna focused on the importance of being an open and welcoming nation.
People from around Wales come to take part in the competitions, ceremonies as well as to relax, socialise and enjoy the main Welsh-language event of the year, which is considered one of the largest cultural festivals in Europe.
A week of worship, music, discussions about faith issues and mission activities, such as 'Open the Book' presentations, will take place in a tent run by people from most Christian denominations.
Looking forward to the week, Bishop Andy said, "For the first time since I became the Bishop of Bangor the 'Prifŵyl' is coming to the Diocese, and there is no better time for the Eisteddfod to be coming to Anglesey.
"The church on Anglesey has really come together as the Anglesey Synod to grasp the new ways of working in our Diocese and to discover what ministry and mission as nine Ministry Areas on the island really entails.
"We've also been working alongside Cyngor Ynys Môn as a partner in two new church school projects, in Holyhead and Newborough, and we are really looking forward to the opening of the first new school in Holyhead next month.
"So there is much to celebrate and give thanks for. Anglesey is an exciting place to be in our Diocese."
As part of its ministry of welcome, the Diocese will be launching and giving out its very own fidget spinner after the worship on Wednesday morning.
The spinner has three arms, one for each part of the Trinity - Father, Son and Holy Spirit - as well as the Diocese of Bangor's motto - Worshipping God, Growing the Church, Loving the World. As the three arms spin, they become one Church.