It was started by the family of Frank Whyte - who died in May aged 69 in a boating accident - as they were left distraught by the state of Spynie Mortuary in Elgin, Moray.
Hundreds of signatures have been collected.
The facility at Spynie is no longer being used for family viewings.
Mr Whyte, from Forres in Moray, died after a boating accident in Findhorn Bay.
His widow, Maryan Whyte, hopes the mortuary situation can be improved.
After the petition handover, NHS Grampian said in a statement: "We welcomed the opportunity to meet with Mrs Whyte today and accept her petition.
"Following Mrs Whyte and her family's distressing experience, permanent alternative arrangements have been put in place in Moray.
"There is now planning under way to address the long-term requirements for Moray, and Mrs Whyte is involved in this process."
Campaigners calling for major upgrades to mortuary facilities across Scotland have handed over a petition to NHS Grampian and Police Scotland.