"For FIFA 21, we’re partnering with Sony and Microsoft to offer you a Dual Entitlement - meaning that you won’t need to buy FIFA 21 twice to upgrade your copy of the game from PlayStation 4 to PlayStation 5, or Xbox One to Xbox Series X," EA explains. "Discless consoles require a digital entitlement to upgrade."
If you own FIFA 21 on PS4 or Xbox One, you'll be able to claim the PS5 or Xbox Series X version of the game for free. This offer will only be available until the release of FIFA 22, which is expected in mid- to late-2021. Don't toss your old disc, though, as you'll need to insert it in the disc drive of your new console (at least on PS5) in order to play the next-gen version.
As EA noted above, digital and disc copies are not interchangeable for the upgrade process. If you're planning on buying an all-digital PS5 or an Xbox Series S, you'll need to own or buy a digital copy of FIFA 21 in order to claim your free upgrade.
Thankfully, FIFA 21 will support cross-progression when the next-gen version arrives this December. This covers "all progress you make or content you acquire within FIFA 21 Ultimate Team (including players, items, coins, FIFA Points, match record, and leaderboard placement), as well as all progression in Volta Football."
Borderlands 3 is offering another free next-gen upgrade to keep on your radar.