The Cottagers beat Derby County 2-0 last night (May 14) to book their place in the final, having narrowly missed out on automatic promotion on the last day of the season.
Villa captain John Terry told Sky Sports: "It's unbelievable and incredible".
Tony Pulis has only won two of his previous nine away games against Aston Villa as a manager, although those wins have come in the past four trips (D4 L3). "We're going to Wembley, let's enjoy it".
Wolverhampton Wanderers and Cardiff were promoted automatically from the League Championship.
Mile Jedinak's first-leg header ultimately settled the tie on Saturday as the sides slugged out a scrappy stalemate at Villa Park.
As a team, Villa made 29 total clearances against Boro, with James Chester contributing the most with seven.
Traore has scored five league goals and assisted 10 others so far this term, and while he is arguably Boro's biggest threat up front, Stewart Downing and 15-goal Britt Assombalonga are also capable of wreaking havoc to Aston Villa's defence.
Boro spent around £50million in the summer to chase an instant return to the Premier League after last year's relegation, but came up short.
Despite initially doing well with both clubs, getting Stoke promoted and keeping West Brom up, fans of the two sides eventually became unhappy with the negative style of play.
The 0-0 draw on Tuesday night extended the run without a home win to 13 games now and it could be a couple more years before another game to get a victor with Villa now one win away from the Premier League.
Bruce was appointed in October 2016, with Villa 19th, and has previously questioned the mentality and ability of some players to handle the pressure.