The Three Lions manager believes that both the Liverpool defender and Manchester United striker will have recovered sufficiently to travel and play in the European Championships
The Three Lions boss began his reign by watching his side narrowly beat Norway 1-0 thanks to a goal from Ashley Young, despite missing a raft of first-team players.
With Johnson among those absent in Oslo, his club understudy, Martin Kelly, has been put on stand-by and made his debut from the bench on Saturday evening.
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Manchester United striker Welbeck is still suffering from the damage caused by a Nigel de Jong tackle when his side met Manchester City in the Premier League in April. He is undergoing intensive ankle treatment and also missed the Norway game.
After the game Hodgson told Sky Sports News: “You know, we've had our doubts during the week, but both of those have taken more and more part in training during the course of the week.
"They're coming back into camp early. Both are coming back on Monday evening rather than Tuesday morning to do a bit of extra work, so basically I'm satisfied with them."
Kelly was brought on for his first cap after Phil Jones was withdrawn complaining about his hamstring, but Hodgson insists that the United defender will be fine.
He added: “Jones was just a bit of tightness in the hamstring which came from running so much I guess."