Woodcock, who has been underwhelming for the Highlanders this season due to injuries and a lack of form, joined the franchise from the Blues at the start of the year.
Despite being fit and available, Mackintosh, 28, has played only five times this season. His last appearance was a start against the Blues in Dunedin on June 1 - a stunning victory for Joseph's men.
The one-test All Black wasn't named in the match-day squad for the recent loss to the Crusaders, a phenomenon he has become all too familiar with this season.
On the face of it, Joseph might not be unduly worried about Mackintosh's departure, but the Highlanders board, which will grill him after a season which has so far reaped only two victories, will not be impressed.
A born-and-bred Southlander, Mackintosh, an affable figure, is popular with supporters but said it was time for a change.
"My whole life I have been a real Southern man and to have the opportunity to work with a new group of guys, experience a new piece of New Zealand and learn about its people is very exciting," Mackintosh said.
"Loyalty is one of my strongest values, so it was a tough decision to leave a franchise that I have always called home. I would like to thank the Highlanders for being a huge part of my life and I will always be very proud to have played for and captained them - it was always a dream of mine growing up.
"In order for me to grow as a player I feel the time is right for me to have a change and I would like thank the Chiefs for showing faith in me and giving me this opportunity."
A big man at 1.93m and 130kg, Mackintosh will join a Chiefs squad with plenty of front row talent, but he is a good replacement for Toby Smith, who is leaving for the Rebels at the end of the season, and will be up against Pauliasi Manu for the loosehead position.
The Chiefs are also well served at tighthead, with recent All Blacks debutant Ben Afeaki and improving man-mountain Ben Tameifuna fighting for the No 3 jersey.
The defending champion Chiefs are sitting pretty at the top of the table ahead of their clash against the ominous-looking Crusaders in Christchurch on Friday.