The pair will join up with the rest of the squad when pre-season training begins on 6 June, and could make their Edinburgh debuts against their previous employers.
Bradley takes his team to Edgeley Park for a pre-season friendly on Friday 19 August (kick-off 7.45pm), a week before Newcastle Falcons visit Murrayfield (Friday 26 August, kick-off 7.30pm) in a tie that will see the first airing of a series of exciting measures designed to improve the match-day atmosphere at the stadium in the new campaign.
Cox brings with him the experience of 64 outings in the English Premiership, a dozen of them in season 2010/11, in addition to 16 appearances in the Heineken Cup and Amlin Challenge Cup.
He has represented England from Schools to under-21 level, and is a former Sale Sharks Breakthrough Player of the Year. Born in Lancaster, the 26-year-old can also play on the flank.
Leck, meanwhile, saw service with Preston Grasshoppers, Calder Vale, Manchester, Sedgley Park before joining the Sharks. The 25-year-old has played 11 times in the Premiership and five times in Europe as well as representing England at under-16 and under-18 level.
Bradley hailed the addition of the players as a "terrific boost" ahead of the resumption of Celtic League and Heineken Cup hostilities. He said: "It's great news for the club that we've secured Sean and Chris and that they'll be here right from the first day of pre-season training in a couple of weeks' time.
"The players are used to the sort of demanding environment and competitions in which Edinburgh operate, and they'll both bring quality and appetite to their respective positions.
"We're still in the process of adding to what is already a strong squad full of international players. What we've got to offer is a team and club committed to continued improvement on and off the field, and it's then a case of identifying the right players and characters to contribute to that progress."
Cox told www.edinburghrugby.org: "I've been really impressed by what Michael has had to say on his vision for the team, and I'm delighted to have become part of his plans. I'm looking forward to getting to know the rest of the lads in the next couple of months and to helping them push on next season."
Leck is equally energised by the prospect of turning out in the black and red, saying: "Edinburgh is a great club and city to be based in, and I'm delighted to have joined. I know all about the quality of player we've got at scrum-half, but I'll be doing everything I can to stake my own claim and repay the faith the club have shown in me."
Sean Cox
Position: lock forward
Date of birth: 16 January 1985
Place of birth: Lancaster
Height: 6ft 5in
Weight: 113kg
Representative honours: England Schools, England under-18, under-19, under-21
Chris Leck
Position: scrum-half
Date of birth: 21 May 1986
Place of birth: Manchester
Height: 5ft 9ins
Weight: 88kg
Representative honours: England under-16, under-18
SIGN UP FOR NEW PERSPECTIVES IN SEASON 2011/12
It's a whole new ball game for Edinburgh fans in season 2011/12, as supporters get closer to the on-field action with seating in the east stand and new pitch-side standing areas.
The price of adult (£180) and student/senior citizen (£90) season tickets has been held, while under-18s will pay just £35 to watch the best in Magners League and Heineken Cup rugby.
Buy before 30 June and you could win a hospitality package for ten people at one of our home European matches next season (Terms and Conditions apply).
For more information on the benefits of being an Edinburgh season ticket holder, and to book in for the campaign under new head coach Michael Bradley, visit www.edinburghrugby.org, call 0131 346 5180 or visit the Murrayfield Ticket Centre (just off Roseburn Street) in person.
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