Chrysler earned a net profit of $183 million in 2011; it also reported an operating profit of almost $2 billion, the first since 2005, The Detroit News reported Tuesday.
"It took an incredible team effort to bring about such remarkable results, and you should be proud," Marchionne said Monday in a message to union workers.
The average bonus check for hourly workers will come to $1,500, less taxes and union dues, the newspaper said.
The checks are normally sent in March. This year, the checks should arrive by Feb. 10, a Friday.
"I ask that you continue to demonstrate the strength and courage you have shown to challenge our destiny and revitalize this great company. The future holds enormous opportunity, and it's a challenge that calls for our continued, shared commitment," Marchionne said in the e-mail.