Your second attempt is the right approach:
GRANT EXECUTE ON PROCEDURE myDB.spName TO 'TestUser'@'localhost';
but if that is not working, verify …
a) you (the user from which you are running all these command) have grant rights
[i.e WITH GRANT OPTION]. If you are root, then you have grant rights.
b) the user exists to which you are granting execute permission e.g.
select user from mysql.user where user like 'test%';
If not, then create the user e.g.
CREATE USER 'TestUser'@'localhost' IDENTIFIED BY 'passwordxxxx';
#depending on your needs
GRANT SELECT,DELETE,UPDATE PRIVILEGES ON myDb.* TO 'TestUser'@'localhost';
Hope this helps 🙂