Jennings, who is set to make his England Lions (A side) debut against the United Arab Emirates in Dubai on Thursday, replaces Lancashire's Haseeb Hameed, who is to return home after fracturing a finger in the third Test defeat in Mohali.
Dawson, the Hampshire all-rounder, who was also selected for the Lions programme this winter before being released to play for Rangpur Riders in the BPL, has been called up to replace Surrey's Zafar Ansari, who is still struggling with the back injury he sustained in the second Test defeat in Visakhapatnam.
Ansari will stay with the squad and continue to receive medical support in India before returning to England on December 8.
Jennings, 24, made his Durham debut in 2012 and was the leading run-scorer in the 2016 Specsavers County Championship season with 1,548 at an average of 64.
He has been on the Lions programme for the last month, initially at the Performance Centre in Loughborough and for the last two weeks in Dubai, based at the ICC Academy.
He is due to join the England squad in Mumbai on December 5 when they begin preparations for the fourth Test which starts at the Wankhede Stadium three days later.
Dawson, 26, made ODI and T20 debuts for England last summer after impressing on last winter's Lions programme in the UAE. He is also expected to arrive in Mumbai early next week.