South Africa seamer Nel could join Essex in time for their opening County Championship fixture against Northants in April 16 - subject to the receipt of a work permit and formal permission from Cricket South Africa.
Nel's arrival could however be delayed until the end of the month should his current side Nashua Titans reach the final of the Standard Bank Pro20 Series on April 25.
He will leave Essex on May 18, with Pakistan leg-spinner Kaneria returning for his fourth spell at the club three days later.
Nel, 30, enjoyed two short stints with the county in 2005 and 2007, taking 14 wickets and said he is delighted to be returning for the beginning of the season.
"I enjoyed my time at the club in 2007 immensely and can't wait to rejoin the boys for the first game. I look forward to giving my all in an early season burst for the Club," said Nel.
First-team Coach Paul Grayson said: "Danish wanted a bit of time at home with his family, which means he misses the first month of the season, and we respect that.
"We've got a terrific replacement in Andre Nel, although we are unsure as to how long he will be available to us at the moment.
"This will be Andre's third spell with us and he's proved a very popular character in our dressing room, who is comfortable in our environment.
"Everyone at Essex is delighted he is coming back and we look forward to him making a positive impact while he is here."