The 47-year-old, who is currently the Bishop of Tewkesbury, will take over from the recently-retired Tim Stevens.
Bishop Snow, who will undertake the role from Spring 2016, said the job was "a little daunting... but exciting".
The Dean of Leicester, the Very Reverend David Monteith, said he was "ideally placed" to serve the diocese with "wisdom, imagination and love".
Bishop Snow is married with three children and is the youngest serving bishop in the Church of England.
He has been the Bishop of Tewkesbury since 2013 and his ministry has taken him to Sheffield and West Africa.
Bishop Snow said he hoped his experience "will be very useful as I come to this very diverse place".
"For us to model, at a local level, how different faith communities can live well together and work in partnership for the common good, that has to be a priority for me.
"I look forward to meeting other faith leaders in the coming weeks."
"I'm very aware It'll take me a while to build relationships and trust," he added.
In July, Tim Stevens, sometimes criticised for being "too political", held his last service ahead of retirement after 16 years as Bishop of Leicester.
During his career, he was widely commended for his work on inter-faith relations. He also led the re-interment service for Richard III earlier this year.
The Right Reverend Martyn Snow has been named the new Bishop of Leicester.