The partnership will run for an initial four years and aims to raise £1.3m and plant around 450 acres of woodland in the UK.
The Woodland Trust owns 50,000 acres of woodland, all of which are open to the public.
The environmental programme will see Ikea donate 10p to the Woodland Trust each time a customer uses their Ikea Family card at 15 stores around the UK.
Ikea said that since its launch in February, more than a million people have joined its family card programme, which gives discounts and exclusive offers to members.
Charlie Browne, Ikea UK's environment manager, said the initiative was an easy way for customers to donate a square foot of forest each time they swiped their Ikea Family card.
He said: "The UK is one of the least wooded countries in Europe so that's one very good reason for doing something positive."
Sue Holden, Woodland Trust's chief executive, said: "Our exciting campaign will make a huge difference to the environment right here in UK, creating hundreds of acres of native woodland and involving thousands of IKEA customers."
Internationally, Ikea offsets its forestry usage by working with the Global Forest Watch and the World Wild Life Fund to support the preservation of natural forests.