A resident of the Flanders section of Mount Olive Township, New Jersey, Brown attended Pope John XXIII Regional High School in Sparta, New Jersey. He missed his sophomore season after breaking his ribs in the first game. He had 41 receptions for 630 yards and six touchdowns as a junior. In his final year he recorded 41 receptions for 857 yards, 14 receiving touchdowns and 7 rushing touchdowns, helping his team reach the non-public league Group 3 final and receiving All-New Jersey honors by the Newark Star-Ledger. He committed to Ohio State University to play college football. He finished with over 3,000 all-purpose yards and 42 touchdowns, after playing at wide receiver, running back and kick returner.
Brown played in all 14 games, including the 2015 College Football Playoff National Championship victory over Oregon, as a true freshman at Ohio State in 2014. He had one reception for nine yards and one run for a 4-yard loss, while playing wide receiver, H-back and special teams. The next year, he excelled in spring practice and was expected to earn the starting wide receiver job, until suffering a broken left tibia and fibula late in fall camp during a non-contact drill, forcing him to redshirt for the 2015 season. The injury was serious enough to require two separate surgeries. In 2016, Brown returned to start in all 13 games as a sophomore. He had 32 receptions for 402 yards and 7 touchdowns. In the third game against the University of Oklahoma, he tied a school record with 4 receiving touchdowns, while totaling 5 receptions for 72 yards. After the season, he decided to forgo his remaining two years of eligibility and enter the 2017 NFL Draft.
Professional career
On January 7, 2017, Brown announced via Twitter that he decided to forgo his senior season and enter the 2017 NFL Draft. Many analysts were surprised he decided to enter the draft and opt out of his last two years of remaining eligibility, due to his limited experience as a one-year starter and his low draft projection. He was one of 58 collegiate wide receivers to attend the NFL Scouting Combine in Indianapolis, Indiana. Brown chose to only perform the three-cone drill, short shuttle, and bench press. He tied for second in the bench press behind Shepherd'sBilly Brown who had 23 reps, but ended up playing tight end in the NFL. On March 23, 2017, Brown attended Ohio State's pro day, along with Marshon Lattimore, Gareon Conley, Raekwon McMillan, Curtis Samuel, and five other prospects. He only performed the 40-yard dash, 20-yard dash, and 10-yard dash as scouts and team representatives from all 32 NFL teams looked on, including head coaches: Bill Belichick, Mike Tomlin, Hue Jackson, Mike Mularkey, Sean Payton, Jim Caldwell, and Marvin Lewis. At the conclusion of the pre-draft process, Brown was projected to be a fifth or sixth round pick by NFL draft experts and scouts. He was ranked as the 27th best wide receiver prospect in the draft by NFLDraftScout.com. The Dallas Cowboys selected Brown in the seventh round of the 2017 NFL Draft. He was the 31st wide receiver drafted in 2017 and was the second wide receiver selected by the Cowboys after North Carolina'sRyan Switzer. Dallas Cowboys' owner Jerry Jones stated that running back Ezekiel Elliott was the main reason they drafted Brown after Elliot continually advocated for him and convinced them he had a lot of talent to bring to the team. Brown was teammates with Elliot at Ohio State.
On September 3, 2018, Brown was placed on injured reserve after missing the preseason with a hamstring injury. He was activated off injured reserve on November 9 to the active roster. Noah was mostly used for his blocking abilities appearing in 8 games with 2 starts, registering 5 receptions for 54 yards total.
2019
Brown began training camp on the physically unable to perform list, because of an offseason left knee surgery. He was placed on the reserve list to start the season on August 31, 2019.