The Ukraine international winger was suspended for four years after failing a 2024 drug test that revealed the presence of a low concentration of meldonium, a prohibited substance.
He was cleared on Friday to resume his career after the Football Association and the World Anti-Doping Agency "resolved his appeal".
"We are happy, especially for him, because we are not able to understand what he has been through in this time and how he feels at the moment," Alonso said in Sydney.
"We want him to feel part of the team, because he has not had this for a long time, and that he has the support from everyone: from the club, from the teammates, from the staff.
"To be honest, we were not expecting to have this great news at this moment, so we are very happy learning that he will be here with us."
Mudryk will join Chelsea for the next leg of their pre-season tour in Hong Kong where they face Juventus on Wednesday, Alonso said, after a 2-1 defeat to London rivals Tottenham in Sydney on Saturday.
But the Spaniard cautioned that Mudryk's reintegration would be a slow process.
The 25-year-old, who joined Chelsea from Shakhtar Donetsk for £62 million in 2023, has not played since November 2024.
"It will take time," Alonso said. "But once there's a change, things will start moving, and for him, it's a massive change (from) training on his own every day.
"I think that had to be really, really hard because he wanted to play football, he wanted to be part of the team, and he was not allowed to do that for such a long time.
"So once this meeting has happened, now we can move on and after we will see if he makes progress quicker or slower. But we need to do the work."
Tottenham boss Roberto De Zerbi managed Mudryk at Ukrainian club Shakhtar Donetsk and was also happy to see him back.
"He's my son, he's a cool guy, a top player, hopefully he can show what he suffered the last two seasons in this coming season, maybe not against Tottenham, but he's a lovely guy," said the Italian.
Mudryk filed his appeal with the Court of Arbitration for Sport and changes to WADA procedures in the interim meant that had his failed test produced the same result now, charges would not have been brought.
Get ready for the new Premier League season
The Premier League returns on Friday, August 21st as defending champions Arsenal host new boys Coventry in the 2026/27 curtain-raiser.
Get ready for kick-off ahead of the new season:
- Transfer Tracker: All the latest done deals and rumours
- Premier League fixture list revealed for 2026/27
- All Premier League and top European club kits for the 2026/27 season
