The 31-year-old returned to Tyneside earlier in the month after overcoming a cancer scare.
Gutierrez will now restart his playing career in the Premier League Cup clash at Whitley Park.
The Argentina defender played his last game for Newcastle just under a year ago in the same competition before securing a loan move to Norwich.
Peter Beardsley’s team were taken to extra-time by Crewe in the last round, before Callum Roberts scored twice to seal their passage.
“Jonas Gutierrez will make his comeback for Newcastle United in Monday’s U21 Premier League Cup last-16 tie against West Ham United,” a Newcastle statement read.
“The Argentine ace returned to Tyneside earlier this month after overcoming cancer and, having taken part in training in recent days, will now make his playing comeback against the Hammers as an over-age player at Whitley Park.
“Ironically, Gutierrez made his last appearance in black and white in the same competition just under a year ago, when United beat Leicester City 2-1 at the same venue.”