Unison says the staff are currently employed on band 2 of the NHS Agenda for Change pay scale, but many have carried out clinical tasks, which should be paid at the higher band 3 rate.
Gary Cleaver, Unison Yorkshire and Humberside regional organiser, said: 'This is a fantastic outcome for these hard-working frontline staff, who are delighted the trust has done the right thing.
'There's no doubt the strength of feeling and determination among these workers has played a huge part in such a significant offer being brought to the table.
'Staff can continue to provide outstanding levels of care to patients, knowing they're being paid fairly.'
The trust was unavailable to comment at the time of writing.