Engelhardt and his wife Diane told staff at the Cardiff-headquartered insurer they will give £1,000 as a personal gift to every full-time employee with at least one year's service and £500 to all other workers.
Admiral employs 8,375 staff, including just over 6,000 in the UK.
The move, which will cost them around £7m, comes less than two months before Mr Engelhardt retires in May after clocking up nearly 25 years at the group he co-founded in 1991.
He will be replaced by co-founder and current Admiral chief operating officer David Stevens.
Engelhardt said: "Saying thank you to all the Admiral staff who work so hard every day to make Admiral great is the most important thing we can do.
"We are making this gift in recognition of the hard work and team spirit that has underpinned Admiral's success as we've grown from a start-up with value of £0 to a FTSE 100 company with a value of £5bn today."
He added that all Admiral staff, from those working in Swansea and Cardiff to workers in Delhi, Richmond or Rome "and all places in-between", will benefit from the gift.
One worker at the group said: "It's amazing. There's smiles all around."
It is the latest cheer for Admiral's workforce after the group confirmed earlier this month it would give staff free shares worth a total of £3,600 each under an employee share scheme following a bumper set of annual results.
The firm posted a 6% rise in group pre-tax profits to £377m for 2015 after boosting UK turnover by 7% to £1.7bn, fuelled by increases in the average premium and a 6% jump in total premiums written for the full year to £1.54bn.
Engelhardt said 2015 was ''the year of the uncut diamond'', in what marked his last full-year results before stepping down.
He added at the time: "When the year started many people thought it would turn out to be a lump of coal. But no, 2015 was no lumpy coal year."