The Leicester-based agency has been briefed to deliver high-impact consumer campaigns that improve customer recognition of the airline across national, regional and overseas audiences.
The hire follows Monarch parting ways with KTA PR in December after a year-long relationship.
Liz Falconer is head of PR & communications at Monarch Airlines, which flies from six bases across the UK to 38 short- and long-haul destinations.
Of Big, she said: "They brought the enthusiasm and creativity I was looking for and demonstrated their understanding both of the fast-paced market in which we operate and Monarch’s service-led brand ethos."
In December Monarch Holdings, which owns Monarch Airways and tour operator Cosmos, announced it expected to post a pre-tax profit of around £15m for 2013.
The figure marks a turnaround from pre-tax loss of £70m in 2011, attributed partly to the Arab Spring and high oil prices.