The 28-year-old has spent the past four years with Danish top-flight club AGF Aarhus.
Hearts head coach Robbie Neilson said: "He's got experience, a good grounding and is a great character.
"We watched a lot of him on video, spoke to various people about him and got good reports and he's impressed in the time he's spent with us."
He works hard and wants to do well
Scotland Under-21 international Kevin McHattie is Hearts' first-choice left-back.
Neilson said: "It's great to get both cover and someone to challenge Kevin."
Eckersley, capped by England Under-18s, made a solitary first-team appearance while at Old Trafford, and had loan spells at Royal Antwerp, Brondby, Barnsley and Port Vale.
The latter resulted in a permanent move to the Valiants, but he switched to Horsens in the Danish top flight in 2008 before moving to Aarhus two years later.
He won the Danish First Division, the country's second tier, with both clubs.
"He works hard and wants to do well," said Neilson on Hearts' website.

Ingram was Most Valuable Player in the domestic T20 Blast in 2016 and has hit two centuries in 2017.
He has previously played in the Indian Premier League for Delhi Daredevils.
The 32-year-old left-hander will play limited-overs cricket for Glamorgan in 2018 and 2019 but will give up Championship cricket.
Glamorgan face Leicestershire in Cardiff on Wednesday in the quarter-finals of the T20 Blast.
Adelaide Strikers are coached by former Australia fast bowler Jason Gillespie, who had a season with Glamorgan and has also coached Yorkshire.
"The decision was made that we'd look over the world for an overseas batsman and we found a quality one in Colin," Gillespie said.
"He gives it a whack... he has a lot of T20 experience and adds a great deal to our batting line-up."
The Big Bash competition starts in December and Ingram's participation will not clash with Glamorgan commitments.

The local development plan is looking at how the area will grow after 2016 and the potential for 14,000 new jobs being created.
Consultation is expected to start in December on 100 sites which could be earmarked for development.
However, final details will not be decided until Spring 2015.
The plan proposes development areas:
Developments in the past have involved transforming the maritime quarter, the docklands for the SA1 housing and the lower Swansea valley.
But the council admits that regenerating existing sites would not provide for all the city's future needs and it will need "significant additional - primarily greenfield - land for development".
As well as "strategic" development sites for more than 500 homes and in some cases up to 1,000 homes, some existing housing areas will be expanded with up to 400 new homes.
The city currently has a population of around 240,500 supporting 107,000 jobs.
It expects over the next 10 years to be the economic hub and main driver of the new Swansea Bay City Region, which held its first meeting this week.
Robert Francis Davies, cabinet member for enterprise, development and regeneration, said: "Swansea is a city which is constantly developing.
"We know that the population will increase significantly in the coming years and we need to ensure that this city can develop in the right way, providing adequate space for housing and for economic growth."
Councillors will be asked to put the next stage of the Local Development Plan (LDP) out to a month-long consultation.

Castell Henllys Iron Age Village, near Crymych, needs people to support the prehistoric site, which is owned and run by the Pembrokeshire Coast National Park Authority.
It would involve practical tasks such as maintaining the herb garden and supporting events.
An open afternoon for those interested was held on Saturday afternoon.
Hearts have signed former Manchester United youth-team full-back Adam Eckersley after a successful trial.
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Glamorgan batsman Colin Ingram has signed for Adelaide Strikers and will play in Australia's Big Bash competition for the first time.
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Residents in Swansea are to be given their say on plans for more than 17,000 new homes across the city.
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Volunteers are being sought to help look after a heritage site in Pembrokeshire.