The promise by Benetton, which has around 6,500 outlets in 120 countries, came in the wake of similar pledges by other global clothing giants Inditex and H&M.
"We have taken the decision to sign the deal on building and fire safety proposed by global union federations IndustriALL and UNI," a Benetton spokesman told AFP.
Inditex, the Spanish firm that owns Zara and other major high-street brands, said on Monday the deal aimed "to enhance health and safety conditions in the textile industry in Bangladesh."
The five-year plan, first launched in 2012, includes appointing an independent chief inspector to "design and implement a fire safety inspection programme that is credible and effective."
Activists had set May 15 as a deadline for signing up to the accord.
The full list of signatories has yet to be revealed, but US-based PVH, owner of the Tommy Hilfiger and Calvin Klein brands, and Germany's Tchibo, were among the first to back it, according to anti-sweatshop network The Clean Clothes Campaign.
The announcements came as Bangladeshi troops wrapped up the search for survivors in the collapsed nine-storey building outside the capital that imploded on April 24th, killing 1,127.
Police have arrested 12 people over the tragedy, including the owner of the building and four factory owners who are accused of forcing staff to return to work a day after cracks emerged in the structure, prompting evacuation.
There are around 4,500 garment factories in Bangladesh, churning out products for Western fashion labels which sell the clothing at many times the cost price.
Hundreds of factories which form the hub of Bangladesh's garment industry are to close indefinitely after worker unrest sparked by the accident, the industry's main trade body in the country said Monday.