Besiktas tried to put up a fight, but were ultimately undone by goals from Ognjen Vukojevic, Andriy Yarmolenko, Oleg Gusev and Andriy Shevchenko as the home side claimed an 8-1 aggregate victory to set up a clash with Manchester City.
The second leg seemed merely a formality for Dynamo, who held a healthy 4-1 lead from the opening leg.
And they wasted no time in adding to that with the opening goal after just three minutes. Gusev provided a neat pass which Vukojevic prodded into the bottom right corner from close range.
Despite the task facing them, Besiktas at least tried to make a contest of it and Ismail Koybasi's 25-yard drive was well held by goalkeeper Olexandr Shovkovskiy.
Bobo then had another opportunity for the Turkish visitors but put his left-footed lob just over the crossbar after 20 minutes.
Dynamo's backline continued to find themselves under threat and Shovkovskiy was called upon again to make another save from Hugo Almeida's header.
Fabian Ernst then tested the Dynamo goalkeeper with a drilled right-footed strike which also warmed the palms of Shovkovskiy.
Chances continued to come Besiktas' way as half-time approached, but Ernst was again unable to add his name to the scoresheet, heading a corner from Guti narrowly wide.
The visitors also enjoyed a bright start to the second half although Shovkovskiy proved equal to a left-footed strike from Matteo Ferrari.
But it was Dynamo who scored again after 55 minutes and very much against the run of play. Andriy Yarmolenko raced on to a through-ball from Artem Milevskiy before nestling a shot into the bottom right corner.
That was enough to knock the fight out of Besiktas, and they were staring another heavy defeat in the face when the Ukrainians scored again nine minutes later.
Roman Eremenko was unfortunate to smash his 25-yard drive onto the post, but Gusev was on hand to put away the rebound from close range.
Shevchenko then completed the scoring after 74 minutes, planting Eremenko's pass into the bottom left corner to wrap up a convincing victory.
Dynamo Kiev 4-0 Besiktas: Match Report - view commentary, squad, and statictics of the game as it happened.