Arnold, who manages a research group at the California Institute of Technology, will serve on the technology giant's nominating and corporate governance committee.
Alphabet said she will receive an initial equity award of $1 million in the form of restricted stock units.
Arnold won the Nobel Prize in Chemistry in 2018 for pioneering science in enzymes and antibodies.
Tilghman, a molecular biology professor, retired from Alphabet's board in February last year.
(Reporting by Amal S in Bengaluru; Editing by Sriraj Kalluvila)
