Navca staff were told about Irvin’s departure on Friday, which was his last day in post.
Neil Cleeveley, deputy chief executive of Navca, has become acting chief executive. His appointment is on an ongoing basis and is expected to be reviewed in the autumn.
A Navca spokesman said the organisation was not advertising for a permanent replacement for the time being.
Irvin was not available for interview but said in a statement that it had been a privilege to be chief executive of Navca and he was looking forward to joining Living Streets in September.
"I hope to extend the local reach of Living Streets, so people have a real say in making their streets safer and easier for walking," he said.
Caroline Schwaller, chair of Navca, said: "I would like to thank Joe for his contribution to Navca and, on behalf of trustees, staff and members, wish him all the best for the future.
"I am delighted that we have someone with Neil’s experience to take up the reins. With the Independent Commission on the Future of Local Infrastructure due to publish its findings at the turn of the year, these are exciting and challenging times for us."