Goals from Aitana Bonmati and Caroline Graham Hansen followed before half-time.
Hayes took off Leupolz at half-time and replaced her with Guro Reiten, giving the team a little more width.
Pernille Harder and Sam Kerr both had good chances to get Chelsea on the board, even if it was unlikely that they could stage a comeback.
But Barcelona were not to be denied, remaining absolutely in control - and brought on former Arsenal stars Vicky Losada and Asisat Oshoala for good measure.
Emma Hayes and her side were left tearful and understandably massively disappointed at the final whistle, but Barcelona were deserving victors.
TALKING POINT - Could Barcelona be the new force in European football?
Barca finished the league season with a +123 goal difference. They've won a record-breaking six domestic titles, but European success has eluded them - with just the one final prior to tonight. Lyon, so long the team to beat, bowed out of the Champions League in the quarter-finals - it's very possible that Barca could now be assembling a dynasty to challenge that great club.
PLAYER OF THE MATCH - Alexia (Barcelona)
The captain led by example all evening, and kept her nerve despite the VAR-induced delay to score the second goal from the spot.
Lieke Martens, Vicky Losada and Alexia Putellas of FC Barcelona celebrate with team mates after their side's first goal, an own goal scored by Melanie Leupolz (Not pictured) of Chelsea during the UEFA Women's Champions League Final match between Chelsea F
Image credit: Getty Images
Chelsea - Berger 6, Charles 5, Bright 5, Eriksson 6, Carter 5, Leupolz 5, Ingle 5, Ji 6, Kirby 6, Kerr 5, Harder 5. Subs - Musovic, Telford, Blundell, England 6, Reiten 6, Fleming, Cuthbert 6, Spence, Andersson, Fox, Beever-Jones.
Barcelona - Panos 7, Torrejon 7, Gujarro 7, Maria Leon 7, Ouahabi 7, Bonmati 8, Hamraoui 7, Alexia 8, Graham Hansen 8, Hermoso 8, Martens 8. Subs - Coll, Font, Laia Codina, Melanie 7, Losada 7, Mariona 7, Crnogorcevic 7, Oshoala 7, Fernandex, Vilamala.
1' GOAL! OH MY GOODNESS, WHAT A START FOR BARCELONA! Martens hit the bar, Chelsea don't clear it, and it looks like it pings off Melly Leupolz and past Ann-Katrin Berger into the net after 33 seconds.
12' PENALTY! Barcelona pressing forward again, and Carter falls over, allowing Carolina Graham Hansen in. She squares it to Hermoso, who's blocked by Leupolz - and the referee points to the spot.
14' GOAL! And Alexia sends Berger the wrong way.
21' GOAL! Oh, Barcelona are playing so, so beautifully. Wonderful passing and movement, and this time it's Bonmati who surges into the box and slides it home.
36' GOAL! Lieke Martens utterly turns Niamh Charles inside out, and plays it to the feet of Caroline Graham Hansen, who taps in.
Chelsea had only failed to score in one of their previous 25 UEFA Women’s Champions League matches.
Barcelona have failed to score in just one of their last 24 Champions League matches.