Bond, who has previously had long spells with Barrow, Colchester and Fylde, joins from Matlock Town.
Jones, meanwhile, has been snapped up on loan from Stoke.
Gavin Cowan, whose charges are going to Darlington tomorrow, said earlier this week that he was hoping to bring in some fresh faces, with Brendon Daniels, Henry Cowans and Courtney Meppen-Walters out.
And 34-year-old Bond brings a wealth of experience, having also played for Chester, Stevenage, Crawley, Chorley and York.
Jones, conversely, comes in to test himself in National League North from Stoke's under-23s.
Telford said on the signings: "Everyone at AFC Telford would like to welcome Eddie and Andy to the club.
"Both players will be available for the fixture at Darlington subject to clearance from the National League and FA."
Meanwhile, the Bucks are one of nine National League clubs to have released a joint statement calling for the resignation of National League chairman Brian Barwick over the allocation of the £10m government rescue package.
They want 'an independent panel to be appointed to review this matter transparently and objectively'.
Fylde, Chester, Dulwich Hamlet, Hereford, Kidderminster, Maidstone, Dorking and Chesterfield are the other clubs involved.
The statement read: "We were disappointed to learn two weeks ago that the National League had allocated these funds based on a subjective judgement of club's needs and not based on lost gate receipts.
"Despite rumours of matters being discussed at sub-committee level of the National League we have received no meaningful communication regarding our request for an independent panel review of the allocation.
"This is an indefensible continuation of apparent disregard for the justified concerns we raise and it is for these reasons we are left with no option other than to immediately call for National League chairman Brian Barwick to resign and an independent panel to be appointed to review this matter transparently and objectively.”