Mr Diamond and group finance director Chris Lucas have agreed to slash their bonus award for 2011 by half, but only if certain performances are not met within the next three years.
The new terms will apply to the £2.7m bonus Mr Diamond was awarded for last year, and the £1.8m bonus Mr Lucas was given.
The banking giant said Mr Diamond and Mr Lucas "volunteered" to subject their bonuses to new conditions in recognition of the "strength of opinion expressed by some shareholders".
The executives hope that the announcement will calm down Barclays' shareholders, whom have shown anger over Mr Diamond's pay package.
In addition, a £5.7m tax payment to Mr Diamond when he moved from the US to London to take the role of chief executive also sparked anger amongst shareholders.
The move threatens to dock Mr Diamond's overall pay for last year by £1.35m.
The chief executive will also reportedly see the long-term incentive part of his pay package fall away, which may see his total package of salary, bonuses and tax benefits slide by 75% to no more than £5.5m.
The bank has agreed the condition and said: "Barclays is fully committed to ensuring that a greater proportion of income and profits flow to shareholders, notwithstanding that it operates within the constraints of a competitive market."
Barclays reiterated that it regards returns produced in 2011 as "unacceptable on an absolute basis".
The bank said it had been in talks with major shareholders since the remuneration report was published on March 9.
The shareholder rebellion over Barclays pay gathered pace earlier this month after leading investor group Pensions & Investment Research Consultants (Pirc) said Mr Diamond should not receive "any bonus at all".
Pirc advised its members to vote against the bank's remuneration report, while Standard Life (Other OTC: SLFPF.PK - news) , Fidelity, Aviva (LSE: AV.L - news) and Scottish Widows, which account for 6.45% of the share register, are expected to do the same.