Yes, you can get Yoshi in Super Mario Odyssey. It’s definitely one of the coolest moments in Super Mario Odyssey (if not any Mario game ever). There’s a few small things that you need to do to find hi, but it’s fairly straight forward.
Firstly, you’ll need to beat the games main storyline. This includes beating Bowser on the Moon Kingdom. You will then unlock the Mushroom Kingdom and Peach’s Castle.
For those that played Super Mario 64, you’ll remember that Yoshi was hiding on the rooftop of Peach’s Castle. Well, guess what? Yoshi is hiding in a little egg on top of Peach’s Castle in Super Mario Odyssey too. You’ll need to throw your cap at the the scarecrow on the left of the castle. This will create a staircase that will allow you to get on top of Peach’s Castle. You can then throw your cap at Yoshi to unleash him. You can’t ride Yoshi, instead you can throw Cappy to capture him. Yoshi can flutter, tongue lick and also eat apples to unlock new areas.
Unfortunately, you can’t take Yoshi outside of the Mushroom Kingdom, but you will find him in certain parts of this level. You’ll need him to complete some of the side missions through the Mushroom Kingdom.
Nonetheless, this was one of the best moments of Super Mario Odyssey. If just discovering Peach’s Castle wasn’t enough, finding Yoshi is just one of many Easter eggs that is available in the Mushroom Kingdom. Yoshi also has a new sticky tongue that allows him to propel to new areas. I’m not sure if he’s ever had this ability before, but it allows him to get to new areas and takes his move-set to the next level.