Edward Loden, who commanded the unit involved in the Bloody Sunday shootings in Northern Ireland, was on holiday when he was shot on Saturday evening.
The attack happened after armed men forced their way into the compound in the Langata suburb.
A family statement described Col Loden as a “devoted family man” and said his death was a “brutal tragedy”.
The BBC’s East Africa correspondent Gabriel Gatehouse said he died on the way to hospital.
Exonerated
A former colonel in the Parachute Regiment, Col Loden served on numerous operations around the world and was awarded the Military Cross for service in Aden in 1967.
In 1972, he was in command of a Parachute Regiment unit that fired more than 100 shots during a civil rights march in Londonderry.
Thirteen civilians were killed at the scene and a 14th victim died from his wounds five months later.
Col Loden was exonerated by the Saville Inquiry into the killings, which said that he did not realise his soldiers might be firing at people who did not pose a threat.
He retired from the Army in 1992, and after following a career in business management, retired to pursue his love of sailing in 1999, his family said.
The statement added: “Edward, married to Jill, father of Jamie and Will, was a devoted family man and proud grandfather of Oliver, Amelia, Joshua, Harry and Emily.
“Jill and her sons would like to say thank you to all the overwhelming messages of love and support from wider friends and family, and request that the family be given time to come to terms with this brutal tragedy.”
The killing comes after the murder of another former British army colonel, David Parkinson, who was killed by an armed gang at his home near Nanyuki, Laikipia, in August.
Col Parkinson, an ex-commander of a base in the area, and his wife were attacked after a gang of suspected robbers, armed with machetes and a gun, smashed their way into the house.