Hundreds of mourners lined the main street in Ecclefechan in south-west Scotland as the cortege left the village ahead of a funeral service in Dumfries.
Cpl Hoole was 26 and a member of The Rifles regiment. He had served two tours in Afghanistan.
He collapsed and died during a training run in Brecon in Mid Wales on 19 July.
A police investigation into his death is continuing.
Before his funeral a hearse was led by a lone piper and carried floral tributes spelling Josh.
The procession then made its way to the Crichton Memorial church in Dumfries, where the coffin was carried by a military bearer party.
Cpl Hoole's brother Tyrone, 27, lined up with Army colleagues to carry the union flag-draped coffin into church.
A military guard of honour stood outside the church and soldiers saluted as the pallbearers filed past.
A piper played a lament outside prior to the start of the service.
His brother also read the eulogy along with his grandfather John Craig and Captain Ian Cullen from the brothers' regiment.
Padre Paul Swinn, Senior Chaplain, The School of Infantry, led the service, which opened with Amazing Grace.
Prayers included the regimental prayer for The Rifles and The Lord's Prayer.
Coldplay's Yellow was played during the service and mourners, including scores of uniformed soldiers, left the church to Wake Me Up When September Ends by Green Day.
The funeral ceremony was followed by a private committal for close friends and family at Roucan Loch Crematorium.
The funeral of Scottish soldier Josh Hoole, who died during an army training exercise in Wales, has been held.