The pair have transferred for an undisclosed fee, with Saturday's fixture against Chorley being their last involvement for Boro.
Left winger Mills, 27, started his career at Derby County, making two appearances for them in the Championship.
He had loan spells at Solihull Moors, Macclesfield and AFC Telford United, where he scored 6 goals in thirty appearances.
When he was released by Derby in 2011, he joined Telford on a permanent basis. After a season there, he went on to play for Worcester City, Boston United and Barrow AFC, before joining Corby Town where Tommy Wright was manager.
He had a prolific goalscoring record at Corby, scoring 53 goals in 110 appearances before he joined Tamworth at the start of the 2016/17 season.
He was at Tamworth for five months before joining Nuneaton, but was initially hindered by injury.
He has amassed an impressive 29 goals in seventy-four National League North games in his career.
He is now back to full fitness, and manager Tommy Wright told his club`s official website: “When he’s fit and flying, he can be unplayable. He is a very exciting player, who as well as creating goals, can score them.
“He scored some great goals for Corby when I was there, and he caused opposing defences no end of problems. He will entertain the fans.”
Trotman (pictured), 20, is a right-back who started his career at Luton Town, but then suffered a broken leg when he was drawing the attention of several other clubs.
When he recovered, he joined St Neots Town and then Loughborough University, from where he was signed by Nuneaton when Wright was manager in the summer of 2017.
Wright added: “He’s a very good defender, who has got terrific pace and is very good at going forward. He’s also one of the nicest lads I’ve ever met.”
Trotman, who played in Nuneaton’s 3-1 home win over Darlington earlier in the season, has also been studying at Loughborough University.