A source tells ESPN's Jeff Passan the deal is worth $800,000 with as much as $200,000 in incentives, including $50,000 each for 40, 45, 50 and 55 games pitched.
Jeffress, 32, is a 10-year veteran who spent the past three seasons with the Milwaukee Brewers. He was released last Sept. after compiling a 5.02 ERA in 48 appearances. He had one of his best years in 2018 when he appeared in 73 games for the division winning Brewers producing a 1.29 ERA to go along with 15 saves.
Jeffress provides veteran help to a bullpen which has gotten much younger over the past 12 months. He and Craig Kimbrel are the lone Cubs relievers with major pennant race and playoff experience.