Reading-born Bridcutt, 23, was joined by Dundee United winger Mackay-Steven and on-loan Hull winger Boyd in getting his first call-up ahead of the World Cup qualifiers against Wales and Serbia later this month. The games at Hampden and in Novi Sad will be the first competitive matches for new boss Gordon Strachan.
Boyd, who is currently on loan with the Tigers from Peterborough, previously featured for Scotland B in 2009 but had never made a full squad.
Southampton left-back Danny Fox has been recalled to the squad, while there is no place for Rangers' Lee Wallace or Phil Bardsley, who has not played for Sunderland since January 19.
Blackpool winger Matt Phillips and QPR forward Jamie Mackie both drop out of the squad as does Celtic captain Scott Brown, whose season appears to be over because of an abductor injury.
In-form Hibernian striker Leigh Griffiths was not included but Chris Burke retains his place after Strachan handed him his first international cap in more than six years in the 1-0 friendly win over Estonia last month.
Bridcutt, who began his career in the Chelsea youth ranks, qualifies through his grandfather from Edinburgh.
The holding midfielder's inclusion is subject to Scottish Football Association paperwork being completed.
Both Strachan and assistant Mark McGhee, a former Brighton manager, have watched him closely.
Strachan said: "Liam is a guy I've been watching. I've seen a lot of his games.
"At the time I didn't realise he could possibly play for Scotland.
"Mark McGhee, who lives in the Brighton area, has seen a lot of Liam and he did his homework into the type of guy Liam was and did he want to play for Scotland.
"We've put that all together and we've come to the conclusion that he's good enough."
Former Scotland Under-21 international Mackay-Steven has returned to top form for United in recent weeks after an injury-hit first half of the season.
Strachan added: "I've seen him a couple of times recently and he makes an impression on the game, that's for sure."
Boyd has scored two goals in three games for Hull since his loan move, which followed an aborted attempt by former Scotland manager Alex McLeish to sign the player during his short reign at Nottingham Forest.
Forest pulled out of a deal to sign the 27-year-old because of the results of an eye test, a decision which played a major role in McLeish's subsequent departure form the City Ground.
Strachan said: "He is an elegant player, a good passer and he scores a fair amount of goals for an attacking midfield player."
The Scotland boss also confirmed Gary Caldwell will be captain in the absence of Darren Fletcher.
Scotland squad to face Wales on March 22 and Serbia on March 26 in World Cup
Goalkeepers: Gilks (Blackpool), Marshall (Cardiff), McGregor (Besiktas).
Defenders: Berra (Wolves), Caldwell (Wigan), Fox (Southampton), Hanley (Blackburn), Hutton (Real Mallorca), Martin (Norwich), Mulgrew (Celtic), Webster (Hearts).
Midfielders: Adam (Stoke), Bridcutt (Brighton), Burke (Birmingham), Commons (Celtic), Dorrans (West Brom), Forrest (Celtic), Mackay-Steven (Dundee United), McArthur (Wigan), Morrison (West Brom), Snodgrass (Norwich).
Forwards: Boyd (Hull), Fletcher (Sunderland), McCormack (Leeds), Maloney (Wigan), Miller (Vancouver Whitecaps), Naismith (Everton), Rhodes (Blackburn).