Matthew Lee, 41, and Severn Vale Housing Society admitted at Gloucester magistrates' court they had failed to ensure the safety of Christine Goodall in her home.
Mrs Goodall, 65, was killed in November 2007 when the boiler behind her fireplace exploded. Her pet dog was also killed instantly in the incident.
It was later found that residual water in the back boiler heated up when Mrs Goodall lit a fire, causing it to explode at the home in Tewkesbury.
Mr Lee and Severn Vale Housing Society admitted to an offence under the Health and Safety Act 1974. They will be sentenced at a later date.
Since the explosion, Severn Vale has carried out around 1,700 inspections to ensure residents are safe. The Health and Safety Executive has warned private homeowners, housing associations and landlords to decommission back boilers.