However, Keane soon encountered problems at his new club, suffering a gash during an EFL Cup tie against Sunderland that ended up becoming infected, leading to a spell in hospital.
Performances for Everton led to him hiding away due to embarrassment too, and he eventually broke down to his family. However, the centre-back has found help through speaking to a sports psychologist, allowing him to "keep on top of it".
"I didn't want to go out, didn't want to see anyone," Keane said in an interview with BBC Sport.
"I felt a bit embarrassed with how things were going on the pitch so I didn't want to be seen anywhere, didn't want to do anything.
"I was keeping it in for a long time, working hard, turning things around on the football pitch but in the end it sort of got on top of me.
"I ended up not having a full breakdown but I was basically in tears telling my family how I felt.
"That was a big breakthrough moment where I sort of got to my 'rock bottom'. From there on I've got better and better with the help of my family and my friends and I started speaking to a sports psychologist which I still do now regularly to just keep on top of it."
Along with the rest of the Everton squad, Keane is waiting to find out when the 2019-20 season will resume.
The Premier League campaign was halted in March due to the coronavirus pandemic, though clubs have returned to training in small groups as part of 'Project Restart' with the target of playing games again in June.
Keane found it "difficult" to be away from his teammates so has relished getting back to work in the last week.
He said: "It's just great to be back around them and see how they're getting on."