The Kroenkes wrote: "We will give everything we've got to win major trophies. And you can rest assured that everyone at the club will continue the hard work to make the coming weeks unforgettable.
"We couldn't have reached this point without the incredible support and backing you have given us once again, and we know you will create another electric atmosphere here tonight. The connection we feel with our supporters fills us with pride."
They added: "Between us, we are building something very special and, wherever this month of May takes us, there will be no standing still when the season ends. We are always forward in our approach, taking the learnings as we go and relentless in the pursuit of progress."
The club spent £250m on eight signings last summer. The windfall of reaching the Champions League final — and potentially winning it — will significantly expand Mikel Arteta's budget for the coming window.
Arsenal's record £691m revenue in 2024-25 has already moved them past Manchester United in the English financial hierarchy, while prize money from a potential Double could add a further £100m-plus to the transfer war chest.
Julián Álvarez, Matheus Fernandes and Valentino Livramento have already been linked with moves to the club, while PSG winger Bradley Barcola has been identified by L'Equipe as the Gunners' primary attacking target.
Arsenal face Crystal Palace on Sunday needing to equal or better Manchester City's result at Bournemouth on Tuesday to be confirmed as Premier League champions. The Champions League final against PSG in Budapest follows on May 30.