Lynn, who was earlier recalled into the team after shoulder surgery ruled him out of the squad a year ago, sustained a calf strain during a Big Bash League (BBL) clash with the Perth Scorchers last week.
The Queenslander was subsequently ruled out of the upcoming ODI series and now White has been named as his replacement.
White's recall in the squad came as a shock as he hasn't played ODI cricket for the national side for almost three years. He played his last ODI against England in January 2015.
The 34-year-old's selection came on the back of his good performance in domestic one-day cricket in recent years and his strong form for the Melbourne Renegades in the BBL.
"He's in very good form as his figures demonstrate, he's playing very well. He's one of the leading run-scorers in the KFC BBL, he's experienced, he's a very smart cricketer and he's a good fielder.He ticks all the boxes for what we need at this stage," cricket.com.au quoted national selector Trevor Hohns, as saying.
White, who has appeared in a total of four Tests, 88 ODIs and 47 Twenty20 internationals for Australia,was the highest run-scorer last season with a total of 457 runs at an average of 76.16, including two centuries and two half-centuries.
The Australia ODI squad is as follows:
Steve Smith (c), David Warner (vc), Pat Cummins, Aaron Finch, Josh Hazlewood, Travis Head, Mitchell Marsh, Tim Paine, Jhye Richardson, Mitchell Starc, Marcus Stoinis, Andrew Tye, Cameron White, Adam Zampa. (ANI)