Mrs. Obama and her daughter arrived at Marivent palace shortly before 1 p.m. and were greeted at the front door of the residence by King Juan Carlos, Queen Sofia and Princess Letizia.
The king, a keen yachtsman, has for decades spent August vacations at the palace with its dramatic cliff-top views of the sea on the Balearic island's southwestern coast near Palma de Mallorca.
Lunch was Andalusian-style chilled gazpacho soup, chargrilled turbot, veal escalopes with mustard, Oriental rice with sauteed mushrooms, a Mallorca-style vegetable ratatouille and sliced fruit with ice cream, accompanied by wines from the northern regions of Rueda and Rioja, the palace said.
The lunch meeting marked the end of a five-day private visit to Spain by Mrs. Obama, who toured beauty spots in the southern region of Andalusia including Marbella, Ronda and the Alhambra palace in Granada.
The king gave Mrs. Obama some seeds for the White House garden as a parting gift, while the queen made a present of handicrafts typical of Mallorca, the palace said.
After lunch the first lady's party was due to fly back to the United States aboard Air Force Two.