The Warriors, relegated last season, claimed a 46-32 aggregate Championship play-off triumph after winning last week's first leg 21-12 in Cornwall.
Leeds, whose Premiership campaign ended with defeat against Heineken Cup finalists Northampton 11 days ago, would have stayed up had Pirates prevailed.
But Worcester, the only Championship club that meet minimum Premiership entry criteria, were in no mood to blow their big chance as a club-record capacity 12,000 crowd roared them home.
Wings Marcel Garvey and Miles Benjamin claimed touchdowns early in each half, while former Leicester and England number 10 Andy Goode crucially kept the scoreboard ticking over through a breakaway try, a drop-goal, penalty and two conversions.
Full-back Rob Cook kicked two penalties for the Pirates and added conversions to centre Drew Locke's score and a late penalty try.
But an uphill struggle they faced before kick-off quickly assumed mountainous proportions as Goode's 15-point haul meant Worcester remained in control throughout, to take the Championship title.
It was Worcester's 31st game of a marathon Championship campaign, but they now return to the Premiership for a second stint among the elite, swapping places with Leeds.
They won 30 of those 31 fixtures, scoring more than 1,000 points in the process, yet the hard work will soon start again as head coach Richard Hill plots next season's Premiership campaign.
Hill made one change to the team victorious in Penzance a week ago, with Scotland international centre Alex Grove preferred to Alex Crockett, while Pirates handed starts to Locke and number eight Kyle Marriott.
The Pirates, 23-21 victors over Worcester in a regular-season game at Sixways seven months ago, took an early lead when Cook found his range with a 30-metre penalty.
Goode quickly landed an equalising strike, and that was the cue for a period of sustained Warriors pressure as they looked to buckle Pirates' resistance.
Worcester, with prop Adam Black and lock Greg Rawlinson making their final appearances for the club, established immediate scrum dominance, and former Gloucester wing Garvey scampered over for a 12th-minute try with the Pirates pack back-pedalling.
Goode converted, and Pirates found themselves 16 points adrift on aggregate approaching the end of a one-sided opening quarter.
A Goode drop-goal then took Worcester further ahead, and although Pirates strung together some threatening passages of play sparked by fly-half Jonny Bentley, they could only add another Cook penalty as Warriors led 13-6 at the interval.
And Worcester wasted little time in the second period to make things safe as Benjamin and Goode both breached Pirates' defence from long range.
The Pirates conjured a touchdown for Locke, assisted by the outstanding Bentley and his Harlequins-bound midfield colleague Matt Hopper, but Worcester had done their job despite leaking a penalty try from a scrum.
With mission accomplished, the final 20 minutes gave Worcester fans a chance to start taking stock of what awaits them next term.
New Sixways arrivals during the summer include former England internationals Shaun Perry and Chris Jones, while experienced Premiership prop Ceri Jones will arrive from Quins.
Hill, though, will be under no illusions at the size of Worcester's task just to retain Premiership status, a challenge that proved beyond Warriors last year when they finished bottom by four points after winning just three of their 22 league games.
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