The 18-year-old Sibley spent nine-and-a-half hours at the crease and faced 484 balls for his double century to become the youngest double centurion in county cricket.
Only WG Grace managed the feat at a younger age in first-class cricket. The Surrey teenager, who returns to sixth-form education on Monday, remains unbeaten on 220 with the hosts – finishing on 572-4 at the close of play – leading Yorkshire by 138 runs.
The previous record for the youngest 200 scorer was set by Northamptonshire's David Sales who scored 210 against Worcestershire at the age of 18 and 237 days in 1996.
"I was so relieved to finally get my 100 but, when I went to 200, it was just unbelievable," Sibley, whose school gave him time off his studies for the match, told reporters.
"I'm not sure what I would have been doing had I been at school today, hopefully it would have been a free period."
Derbyshire's miserable season ended in disaster as their innings defeat to Warwickshire confirmed their relegation.
Chasing Warwickshire's first innings total of 391, Shivnarine Chanderpaul top-scored with 52 but the hosts were made to follow on after amassing just 103 runs. Their second innings continued in the same vein as their first, losing five wickets for just 38 runs. Tom Poynton was the only player to show any resolve, notching 41 off 62 balls, as Notts were beaten by an innings and 168 runs.
Nottinghamshire and Somerset made the best of good overhead conditions as they both learned that their Division One status was secure for another season.
Chasing Nottinghamshire's first innings score of 406, James Hildreth and Nick Compton shone with the bat as the visitors managed 372 in their response – Hildreth eventually falling for 161. In batsmen-friendly conditions, the hosts finished the day's play 173 runs ahead on 139-9.
In Division One's only other game of the day, Durham's Keaton Jennings and Michael Richardson frustrated the Sussex bowlers, putting their side in the lead with a solid batting performance.
Durham's poor first innings score of 164 was trumped by Sussex's 328 – the hosts having a lot of work to do as they took to the crease for the second time. But Jennings and Richardson performed superbly with the bat, leading their team to a 216-run lead, closing on 380-7.
In Division, Two Moeen Ali claimed impressive figures as he tore through the Northamptonshire batting line, inspiring Worcestershire to victory.
Having secured promotion during the previous day's play, the visitors batted like a side with their mind on other matters. Chasing 257 for victory, Northamptonshire fell woefully short of the target, reaching just 141 with Ali claiming six wickets for just 77 runs.
In the division's other fixture, Matt Coles helped Hampshire to beat Essex by an innings and 31 runs.
Adam Wheater and Michael Carberry starred for the hosts, knocking 122 and 85 respectively for their side who an impressive score of 456. In response, the hosts could only muster 207 as they were made to follow on. Sensing victory, Coles claimed four wickets for 83 runs which helped his side to a comprehensive victory.