The Marie Curie Hospice, in Balornock Road, received 'very good' and 'good' grades from Healthcare Improvement Scotland's report.
Inspectors praised the "dedicated" team of workers and said they provided a "very high" care standard.
They also identified areas for improvement, including staff infection control procedures, medication management and the use of adult support and protection procedures.
The inspection visit took place on March 25 and 26, this year.
All of the services offered by the hospice are run to meet the palliative care needs of people with a progressive, life-limiting illness.
The facility has a maximum of 30 inpatient beds, with 21 single en-suite rooms and three triple bedded bays. The day service runs groups on Monday to Friday, for up to 12 people.
Susan Brimelow, chief inspector, said: "Our inspection of Marie Curie Hospice - Glasgow found a dedicated team of staff focused on providing a very high standard of care, treatment and support to patients and relatives.
"Patients spoke highly of the quality of care received and we found good links between the service and local NHS resources, as well as other charitable providers.
"This inspection resulted in four requirements and eight recommendations which Marie Curie Cancer Care must address as a matter of priority. We will follow-up these concerns at future inspections."
Evening Times readers, by supporting our Big Build fundraising campaign, helped towards the cost of building the £16.1million, 30-bed hospice at Stobhill Hospital.
It was officially opened by Prince Charles in June 2011.
As he added his signature to the visitors book, the Prince said a special thank you to the Evening Times and the people of Glasgow who had worked so hard to help raise the £16.1million.
At the unveiling of the hospice, he paid tribute to all of those who had made the project possible.
And during his speech he thanked the Evening Times for its backing of the Marie Curie appeal.
He said: "I would like to thank all of the marvellous people in Glasgow and the whole of Scotland for their generosity.
"And thanks goes to the Evening Times, who stirred up their readers and led a massive fundraising campaign. It was wonderfully generous of so many people to take part."
The Big Build was one of the most ambitious campaigners ever run by the Evening Times and relied on the generosity of readers, their families and friends.
It was a bold collaboration between Scotland's favourite evening newspaper and officials at the cancer charity Marie Curie who were desperate to build one of Europe's best equipped hospices right here in Glasgow.
For three years our big-hearted readers worked tirelessly to raise the golden sum of £8.1m. It was a fantastic achievement which culminated in the opening of the hospice last year.
The old centre, built in 1976, was falling into disrepair. The windows leaked and paint was peeling.There was no piped oxygen on the wards.
Relatives and friends who came to visit had to squeeze into just one family area and there was an acute lack of parking spaces.
A new hospice would cost £16.1m. Charity chiefs secured £8m and turned to the Evening Times in a bid to find the rest.