St Monica's Day Centre and Betty Dodd Day Centre will be decommissioned, according to a report to the borough council's executive.
The closures, along with a reduction in day care places, will save the council £354,000.
Eight jobs will be lost in the reorganisation, although one position was vacant and staff will be encouraged to apply for vacancies in learning disability services, said the report.
Labour Saints councillor Javed Hussain told the executive committee a new programme called 'side-by-side' had been introduced in adult social care.
"This will put great emphasis on a personalised approach and focus on individual needs and interests to achieve better outcomes for older people," he said.
"It will ensure anyone with complex needs, such as advanced dementia, is getting the right support at the right time.
"And it will deliver a service which is more efficient and makes best use of all our resources, while achieving savings as part of the Covid emergency budget.
"This involves the decommissioning of St Monica's and Betty Dodd, and ending the weekend service at Farley Day Centre.
"You will also note the ongoing steady decline in day care attendance, with people taking up other opportunities through side-by-side, which has been very successful.
"We've seen a spiralling loss in people using day care services during the last two years," added councillor Hussain, who's the portfolio holder for people, with responsibility for adult services.
"We've got almost 50 per cent over capacity, so unfortunately we're having to recommend the closure of St Monica's and reduce some of our services."
There were only 55 responses to a council survey about the planned changes, as well as two telephone calls.
Labour Farley councillor Mahmood Hussain warned of a huge impact on the mental health of the elderly from Covid-19.
"We need to take into account those people who are isolated and have little contact with anyone else," he explained.
Councillor Javed Hussain replied: "We've had a number of meetings to discuss mental health issues.
"We're reviewing things with the East London Foundation NHS Trust (ELFT) and we take the growing demand for this extremely seriously."
Labour Lewsey councillor Aslam Khan said: "We need to ensure the infrastructure we put in place with all the social prescription element continues.
"If elderly people haven't got day centres to go to any more, they've got to be doing other things.
"A huge amount of work went into this and we need to ensure the system stays joined up and connected."
Councillor Javed Hussain said: "It's understanding what people's strengths and weaknesses are, what they'd like to achieve and what interests they have so we can meet their needs."
The executive unanimously agreed the savings package to remodel older people's day care in Luton.