Gennett was awarded a raise from $2,525,000 to $5.7 million. The Reds offered $5.1 million.
Players finished with a winning record for the second time in three years, but only their fourth since 1996.
The 22 decisions were the most since players went 14-10 in 1990. Just five players settled among the 27 who swapped proposed salaries with their teams last month.
Gennett hit .295 last year and set career bests with 27 homers and 97 RBI in his first season with the Reds. He hit four homers in a game on June 6.
With many teams adopting "file and trial" strategies, the only players who reached agreements after the Jan. 12 exchange of proposed salaries were Houston outfielder George Springer, Baltimore second baseman Jonathan Schoop, Orioles pitcher Kevin Gausman, Detroit shortstop Jose Iglesias and Pittsburgh reliever Felipe Rivero.