Lancaster, 76, who has recently returned from leading a RHS tour to China, his eleventh visit to the country, said he was "overwhelmed" with the messages of support he had received.
The former Hillier Arboretum curator said the visit was "like flipping through the pages of the Hillier manual".
He said horticulture was "one of the most important professions in the entire world, with what it means to people's well-being".
Lancaster said his personal ambitions were to "keep getting excited about plants and talking about plants" and to keep teaching.
Also in the honours list, Penelope Hobhouse becomes an MBE for services to British gardening. Former Haskins buying director and HTA board member Philip Evason received an MBE for services to the Reserve Forces. And Parkrun founder Paul Sinton Hewitt was awarded a CBE for services to grassroots sport participation.