Fiorentina winger Juan Cuadrado has made it clear he wants to join Chelsea, Sky sources understand.
Johnson fought off competition from 120 applicants to land the role after impressing chairman Simon Corney.
He takes over from Paul Dickov, who departed last month, and inherits a side who currently lie 21st in the npower League One table. He will be in the dugout for Tuesday night's crucial game against fellow strugglers Hartlepool.
The 31-year-old, the son of Yeovil boss Gary Johnson, becomes the youngest manager in the Football League, with the Boundary Park job his first managerial role after a playing career with Yeovil, Bristol City and Kilmarnock.
Johnson takes the reins from caretaker manager Tony Philliskirk, who leaves the League One side two points from safety with two games in hand on the teams above them.
In his playing days, the Suffolk-born midfielder achieved a double promotion in a five-year spell at Yeovil under the management of his father before moving to Hearts in 2006 where he picked up a Scottish Cup medal.
Johnson then re-joined his father at Bristol City, where he celebrated promotion to League One before reaching the 2008 play-off final, losing out to Hull at Wembley.
He ended his playing career at Kilmarnock where he won the Scottish League Cup and now faces an immediate challenge to escape relegation as he follows his father's footsteps into management.