It will be Mahmood's sixth season at Surrey, who won promotion to the first division of the county championship last summer.
Nicholson, who won one Test cap for Australia in 1988, joins after a season at Northamptonshire, where he took 46 wickets at an average of 31.97.
In five seasons at Surrey, Mahmood, 31, has taken 150 first-class wickets at 30.83 and scored 2300 runs at 37.7.
Surrey Cricket Manager, Alan Butcher said on Friday: "I am extremely pleased to have Azhar on board again who has been an excellent servant for us over the past five seasons.
"His ability with both bat and ball is unquestioned and gives us great flexibility in selection while Matthew will bring that added fire to our pace attack that we will certainly need moving into Division One. I'm really looking forward to working with him."