However, the remaining 31 stores will close and about 260 jobs are expected to be lost.
Jones was owned by Alteri Investors, whose "value" shoe chain Brantano collapsed earlier this week.
Endless bought the profitable parts of the business under a "pre-pack" administration deal.
Under a pre-pack agreement, a buyer for a firm or its profitable assets is lined up in advance of the administrators being called in.
"We are delighted that we have been able to rescue such an iconic UK footwear brand as Jones Bootmaker, including a high proportion of stores and preserving a large number of jobs, especially given the current economic pressures faced by retailers across the UK," said Will Wright, partner at KPMG and joint administrator.
"This deal recognises the value of Jones as a strong and popular High Street brand with a loyal customer base."
Alteri Investors acquired Jones Bootmaker and Brantano in October 2015. About four months later, Brantano went into administration and Alteri bought it back, minus a few stores.
The chain subsequently faced "difficult trading conditions", and was put into administration on Wednesday after Alteri failed to find a buyer.
What is a pre-pack administration?
The bulk of footwear chain Jones Bootmaker has been sold to investment firm Endless, saving 72 stores and 840 jobs.