The about-face is the 30th performed by the coalition since it came to power, critics claim.
The charity cap, limiting tax relief at £50,000, was proposed in Mr Osborne’s March Budget.
Charities hailed the climbdown as “a victory for common sense”. However, the move provoked anger from the Tories’ Lib Dem coalition partners, who said it meant the government had dropped an important measure to tax the rich.
Labour said the Budget had become a “shambles” after earlier U-turns over VAT on hot pasties and caravans.