The new £1.2 million facility housing the Enhanced Drug Treatment Service is licensed by the Home Office and will be open between 9am and 5pm each day.
It will run alongside existing homelessness health services in the city.
A specialist team will be supported by other health and social care services, with patients requiring to be committed to the treatment and having to attend the centre twice a day, seven days a week.
On top of treatment for their physical health - including infections, wounds or abscesses - patients will receive a holistic assessment of their social, legal and psychological needs.
Independent evaluation will be carried out on the pilot project, which is expected to treat up to 20 patients in its first year and up to 40 patients in year two.
Susanne Millar, chairwoman of Glasgow's Alcohol and Drug Partnership, said: "Sadly, Glasgow suffered a record number of drug related deaths last year and there was also an increased number of non-fatal overdoses.
"This challenging social issue demands innovative treatments and this gold-standard service is leading the way in Scotland.
"It is aimed at people with the most chaotic lifestyles and severe addictions who have not responded to existing treatments."
She added: "People might question why health services are spending money providing heroin for people with addictions - the answer is 'we can't afford not to'.
"Not only are we are striving to save the lives of individuals themselves, we also aim to reduce the spread of HIV and to reduce the impact of addictions on Glasgow families and communities.
"Successfully treating a person's addiction not only helps them, it reduces pressures on front-line health and criminal justice services while reducing antisocial behaviour and drug related crime in communities."
The injectable opiate - or heroin-assisted - treatment will only be available to patients already involved with Glasgow's Homeless Addiction Team.
Suitability for the treatment will be assessed and anyone meeting the criteria will receive a prescription for pharmaceutical-grade diamorphine injections.
These must be injected in a secure clinical room under the strict supervision of, and observed by, trained nursing staff.
It is hoped the centre will help plans for a drug consumption facility to also open in Glasgow, allowing a safe, clean place where people could use their own street drugs in the presence of trained medical staff who could react in the event of an overdose.
Dr Saket Priyadarshi, senior medical officer at Glasgow Alcohol and Drug Recovery Services, welcomed the new Enhanced Drug Treatment Service.
He said: "This is a much needed and welcome addition to the comprehensive treatment and care services already existing in Glasgow.
"We have known for a number of years that there are people who continue to experience harm despite receiving conventional treatment.
"It is only appropriate that, as in other branches of medicine, we can offer addictions patients the next line in treatment.
"Heroin-assisted treatment is a highly evidence-based intervention and it will be delivered with intensive psycho-social support to address the wide range of harm and social care needs that this population experiences."