The organisation builds gardens in children's hospices. It is hoped the move will enable it to focus on developing its existing programme of fundraising and garden building while adding new initiatives.
The HTA will take on the administrative and financial systems, and use its publicity-generating machine to increase awareness of Greenfingers' activities.
HTA president Andrew Richardson said Greenfingers was an important and successful charity and the HTA was in a good position to help secure and develop its operations and increase its publicity.
Greenfingers Appeal chairman Richard Jackson said the move would place the organisation in an "excellent position" to expand operations.