The Spanish defender joins on a two-year contract and becomes the club's fourth signing under Rafa Benitez since their relegation from the Premier League.
Gamez is a full-back comfortable on either flank and brings experience to a defensive group that lost captain Fabricio Coloccini earlier this month.
The 31-year-old captained Malaga before leaving for Atletico two years ago.
"I am really looking forward to starting the next part of my career at Newcastle," he told the club website. "It was the right time to leave Atletico Madrid and this is the right move for me.
"We have an exciting project here, to bring Newcastle back to where it belongs, in the Premier League, and I am very happy to be a part of that."
Benitez said: "I am really pleased to bring Jesus here to Newcastle. He is a very good defender who can play on both sides, left and right.
"He is experienced, I know he has great character and, importantly, he is an excellent professional. I am sure he will give balance to the team."
Gamez is expected to join new arrivals Dwight Gayle, Matt Ritchie and Matz Sels on a pre-season trip to Ireland this weekend.
Newcastle’s confirmed pre-season fixtures:
Sun 10.07.2016: U21s v Bradford Park Avenue (a) @ Horsfall Stadium, 3pm. Friendly.
Sat 16.07.2016 Bohemian (Ireland) (a) Dalymount Park, Dublin, 2pm. Friendly. ST holder sale now, £12.50 adults, £8.50 concessions (over 60s/ students), £4 U16s.
Sun 16.07.2016: U21s v Darlington (n) @ Northern Echo Arena, 3pm. Friendly.
Wed 20.07.2016 Doncaster Rovers (a) Keepmoat Stadium, 7.45pm. Friendly. ST holder sale now, £10 adults, £5 concessions (over 60s/17-21s) £1 U16s. U16s get in free if purchased with an adult ticket (not available online, one free ticket per adult ticket purchased).
Sat 23.07.2016 Sporting Lokeren (Belgium) (a) Daknam Stadium, 4.30pm local time. Friendly. Ticket details tbc.
Sat 23.07.2016 U21s v Corby Town (a) @ Steel Park, Corby, 3.30pm. Friendly.
Sun 24.07.2016 U21s v PSV Eindhoven (n) @ Steel Park, Corby. Noon. Friendly.
Mon 25.07.2016 U18s v Fermanagh (n) @ Ballymena, 7.30pm. NI Super Cup.
Tue 26.07.2016 U18s v Right to Dream (n) @ Seahaven, Portstewart, 7pm. NI Super Cup.
Tue 26.07.2016 Southend United (a) Roots Hall, 7.45pm. Friendly. Member sale now, £12 adults, £5 concessions (over 60s/17-21s), £2 U16s.
Wed 27.07.2016 U18s v Tyrone (n) @ The Warren, Portstewart, 3.30pm. NI Super Cup.
Thu 28.07.2016 U18s v opponent tbc, location and kickoff tbc. NI Super Cup.
Fri 29.07.2016 U18s v opponent tbc, location and kick-off tbc. NI Super Cup.
Sat 30.07.2016 Vitesse Arnhem (h) SJP, 3pm. Friendly. Public sale now. £15 adults, £5 concessions. Only selected parts of lower bowl on sale initially.
Sat 30.07.2016 U21s v York City (a) @ Bootham Crescent 3pm. Friendly.
Mon 01.08.2016 U21s v Ashington (a) @ Woodhorn Lane, 7.30pm. Friendly.
Mon 01.08.2016 - Fri 05.08.2016 U16s v Charlton Athletic, Seattle Sounders (USA), Friendly Academy (Zimabwe). Youdan Trophy, Sheffield (games 30 mins x 2).
AUGUST
Friday 5: Fulham (a) (7.45pm)
Saturday 13: Huddersfield Town (h) (3pm)
Wednesday 17: Reading (h) (7.45pm)
Saturday 20: Bristol City (a) (3pm)
Saturday 27: Brighton (h) (3pm)
SEPTEMBER
Saturday 10: Derby County (a) (3pm)
Tuesday 13: Queens Park Rangers (a) (7.45pm)
Saturday 17: Wolves (h) (3pm)
Saturday 24: Aston Villa (a) (3pm)
Wednesday 28: Norwich City (h) (7.45pm)
OCTOBER
Saturday 1: Rotherham United (a) (3pm)
Saturday 15: Brentford (h) (3pm)
Tuesday 18: Barnsley (a) (7.45pm)
Saturday 22: Ipswich Town (h) (3pm)
Saturday 29: Preston North End (a) (3pm)
NOVEMBER
Saturday 5: Cardiff City (h) (3pm)
Saturday 19: Leeds United (a) (3pm)
Saturday 26: Blackburn Rovers (h) (3pm)
DECEMBER
Saturday 3: Nottingham Forest (a) (3pm)
Saturday 10: Birmingham City (h) (3pm)
Tuesday 13: Wigan Athletic (a) (7.45pm)
Saturday 17: Burton Albion (a) (3pm)
Monday 26: Sheffield Wednesday (h) (3pm)
Saturday 31: Nottingham Forest (h) (3pm)
JANUARY
Monday 2: Blackburn Rovers (a) (3pm)
Saturday 14: Brentford (a) (3pm)
Saturday 21: Rotherham United (h) (3pm)
Saturday 28: Brighton (a) (3pm)
FEBRUARY
Wednesday 1: Queens Park Rangers (h) (7.45pm)
Saturday 4: Derby County (h) (3pm)
Saturday 11: Wolves (a) (3pm)
Tuesday 14: Norwich City (a) (7.45pm)
Saturday 18: Aston Villa (h) (3pm)
Saturday 25: Bristol City (h) (3pm)
MARCH
Saturday 4: Huddersfield Town (a) (3pm)
Tuesday 7: Reading (a) (8pm)
Saturday 11: Fulham (h) (3pm)
Saturday 18: Birmingham City (a) (3pm)
APRIL
Saturday 1: Wigan Athletic (h) (3pm)
Wednesday 5: Burton Albion (h) (7.45pm)
Saturday 8: Sheffield Wednesday (a) (3pm)
Saturday 15: Leeds United (h) (3pm)
Monday 17: Ipswich Town (a) (3pm)
Saturday 22: Preston North End (h) (3pm)
Saturday 29: Cardiff City (a) (3pm)
MAY
Sunday 7: Barnsley (h) (12pm)