The Tigers currently lie fifth in the Guinness Premiership and topped their pool in the Heineken Cup, giving them a home quarter-final against Bath in April.
Meyer, the only man to have led sides to success in each of the Vodacom Cup, Currie Cup and Super 14 titles in South Africa, thanked Leicester for their support.
"Leicester are a very special rugby club and I accepted the job there because I felt they were equipped to go on to greater success," he said.
And Tom added that Heyneke made the decision with the club's full support.
"We could all sense success with Heyneke as head coach. He has an outstanding record of achievement in his career," he stated.
"He had the club's full support to remain in South Africa for as long as necessary in such difficult circumstances.
"Heyneke is a very honourable man and, after discussing the situation with his family, he felt it unfair on both parties to carry on indefinitely.
"While disappointed he is unable to carry on the good work here, we wish him and his family well. They will always be welcome at Leicester."
Bookmark with:
What are these?