Republic of Ireland international Hourihane, 31, arrives on a two-year deal after his contract at Aston Villa expired at the end of June.
Chester, 33, joins on a one-year deal after being released by Stoke City.
McGoldrick, 34, has also signed a one-year contract following his departure from Sheffield United.
The former Barnsley captain said he was looking for "something that was going to excite me" after his five years with Villa came to an end earlier in the summer.
"Fortunately enough for myself, I have played all the way up from League Two to the Premier League so analysing it this summer as a free agent, I was thinking what do I want next and what do I want to achieve and be part of," he told the club website.
"Derby ticked all the boxes.
"Everyone knows the difficulties here over the last couple of years but it's a fresh start, new takeover and the excitement is here and that's why I'm here and want to be a part of it."