The association's general secretary, Brian Strutton, says that "given Ryanair's previous hostility towards unions, today's agreement is an historic one".
"We now call on these unions to stop wasting time and act quickly to deliver 20% pay increases to our pilots in February, and conclude formal recognition agreements, which they are presently sitting on", he said.
Eddie Wilson, Ryanair's head of personnel, welcomed the move to formally recognise the union. The Ryanair stock has improved pretty steadily since it stated its intention to recognise pilot unions for the first time in its history.
Confirming the deal on Tuesday, the carrier said Balpa would now be the sole representative body for Ryanair-employed pilots in the United Kingdom, one of its biggest markets.
Ryanair's decision marks a historic turning point for the company, according to industry analysts.
Independent aviation analyst John Strickland described Tuesday's announcement as "a major strategic change for Ryanair". The pilots had initially rejected the offer over concerns about pilot staffing, after Ryanair suffered shortages starting last Autumn, and about employment terms and conditions.
"Pay increases and union recognition still leave them with much lower costs than competitors".
"Things have had to change and O'Leary has been forced to accept that the pilots have more power", Wilson told AFP.
The turmoil comes as the European aviation sector also continues to face turbulence from Brexit.
Ryanair has previously been reluctant to deal with unions.