IRS says:
Why your coronavirus check won't get taxed
Before the final bill language was available, there was some uncertainty about several aspects of the coronavirus stimulus package and how people would receive money. The version of the bill that the Senate passed calls the financial assistance "2020 recovery rebates" and structures them as a tax credit. The coronavirus checks that people will receive will technically be an advance refund of that recovery rebate credit.
Because of that structure, the coronavirus check won't be considered taxable income. Instead, it'll simply reflect an adjustment to the amount of income tax you otherwise would've owed. At the same time, because the tax credit is refundable, it won't matter if you have tax liability or not -- you'll still be able to claim it.