The Tottenham Hotspur left-back returns to the senior set-up after withdrawing from the previous squad in November due to injury.
Udogie, 21, has earned just two international caps with the Azzurri since October and is one of four Premier League players in Spalletti's latest squad along with Spurs teammate Guglielmo Vicario, Arsenal's Jorginho and Aston Villa's Nicolo Zaniolo.
Vicario, who is yet to make his senior debut for Italy, will compete with current number one Gianluigi Donnarumma, Alex Meret and Marco Carnesecchi, another uncapped shot-stopper, for a start between the sticks.
Meanwhile, Torino wing-back Raoul Bellanova, Hellas Verona midfielder Michael Folorunsho - on loan from Napoli - and Udinese striker Lorenzo Lucca - on loan from Pisa - have all receive their first senior call-up to the Italy squad.
Bellanova, who has been linked with Manchester United in recent weeks, has been a standout performer for Torino this term, contributing with one goal and five assists in 27 Serie A outings to help the club climb to 11th in the table.
The 23-year-old has been rewarded with his first Italy call-up having previously made over 80 youth team appearances for the Azzurri from Under-15 to Under-21 level.
Folorunsho, meanwhile, has starred on loan at relegation-threatened Verona and has particularly impressed since the turn of year, scoring three goals and providing one assist in his last seven Serie A matches.
The 26-year-old, who is of Nigerian descent, most recently netted the winning goal for Verona in a narrow 1-0 away victory over Lecce last weekend.
As for Lucca, he is Udinese's top scorer this season with eight goals in 30 appearances, netting his seventh Serie A strike of the campaign in last weekend's 2-1 win at Lazio.
The 23-year-old striker has received his first international call-up of any kind since representing Italy's Under-21s in November 2022.
Lucca is one of seven attacking options selected by Spalletti along with Zaniolo, Federico Chiesa, Riccardo Orsolini, Giacomo Raspadori, Mateo Retegui and Mattia Zaccagni.
Sassuolo's Domenico Berardi is a notable absentee as he is sidelined with a long-term Achilles injury that is set to see him miss Euro 2024, while Lazio captain Ciro Immobile has once again been overlooked after also missing out on a call-up during November's international break.
Lorenzo Pellegrini also missed out in November, but the Roma skipper returns to Spalletti's set-up this month and will battle with Jorginho, Folorunsho, Nicolo Barella, Giacomo Bonaventura, Davide Frattesi and Manuel Locatelli for a place in midfield.
At the age of 36, centre-back Francesco Acerbi is the oldest member of Spalletti's squad, while Inter Milan teammates Alessandro Bastoni, Matteo Darmian and Federico Dimarco are among the defenders to earn a call-up.
Italy will face Venezuela at a neutral venue in Florida on March 21 before travelling to New York to take on Ecuador three days later.
Italy's 28-man squad in full:
Goalkeepers: Marco Carnesecchi (Atalanta BC), Gianluigi Donnarumma (Paris Saint-Germain), Alex Meret (Napoli), Guglielmo Vicario (Tottenham Hotspur)
Defenders: Francesco Acerbi (Inter Milan), Alessandro Bastoni (Inter Milan), Raoul Bellanova (Torino), Alessandro Buongiorno (Torino), Andrea Cambiaso (Juventus), Matteo Darmian (Inter Milan), Giovanni Di Lorenzo (Napoli), Federico Dimarco (Inter Milan), Giorgio Scalvini (Atalanta BC), Destiny Udogie (Tottenham Hotspur)
Midfielders: Nicolo Barella (Inter Milan), Giacomo Bonaventura (Fiorentina), Michael Folorunsho (Hellas Verona), Davide Frattesi (Inter Milan), Jorginho (Arsenal), Manuel Locatelli (Juventus), Lorenzo Pellegrini (Roma)
Forwards: Federico Chiesa (Juventus), Lorenzo Lucca (Udinese), Riccardo Orsolini (Bologna), Giacomo Raspadori (Napoli), Mateo Retegui (Genoa), Mattia Zaccagni (Lazio), Nicolo Zaniolo (Aston Villa)