Terms of the deal were not disclosed for Tavecchio, who was released by the Oakland Raiders earlier this month.
Tavecchio will battle Matt Bryant for the kicking responsibilities with the Falcons.
The 28-year-old Italian replaced Sebastian Janikowski in 2017 and made 16 of 21 field-goal attempts — including three from at least 50 yards — during 16 games in his lone season with the Raiders. He connected on 33 of his 34 extra-point attempts.
Tavecchio was expected to be the Raiders’ kicker this season, but competition for the job will be between Mike Nugent and Eddy Pineiro.
The left-footed Tavecchio has also spent time with the San Francisco 49ers (2012), Green Bay Packers (2013) and Detroit Lions (2013-14).
Bryant has been nursing an undisclosed leg injury through training camp and sat out the first three preseason games. The 43-year-old returned to the field on Saturday, making field goals from 47 and 43 yards in the Falcons’ 17-6 loss to the Jacksonville Jaguars.
Bryant, who is the Falcons’ all-time leading scorer, converted 34 of his 39 field-goal tries last season and all 35 of his extra-point attempts.