The 27-year-old spent last season recovering from an injury sustained on the final day of the previous campaign.
He scored a diving header for the Jambos in their 7-0 friendly win over East Fife on Tuesday.
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Discussing his performance, Hearts manager Robbie Neilson said: "I liked what I saw, so he needs to keep that up. He'll keep playing and training."
Former Wales U21 international Wright will have another chance to impress Neilson when Hearts take on local side Spartans FC tonight.
“He'll be involved in that a little bit and then there's the game on Saturday, so we'll see how he does,” the Jambos boss added.
"We spoke to him a while ago and obviously he got quite a bad injury and was in rehab. He's just coming back."
Wright was previously close to a move to Hearts at the end of his Rovers contract in 2021.
But the move broke down after he suffered severe damage to both his knee and ankle against Peterborough United in May of that year.
He has not played competitively since and was assisted in his rehabilitation by Doncaster last term.
Both parties agreed to maintain an open dialogue about a potential contract extension for Wright, who previously failed to reach an agreement with the club.
The Huddersfield academy graduate spent five seasons with Doncaster, making 157 appearances in all competitions.
Wright could end up playing in Europe next season after Hearts qualified for the Europa League play-off round following their third-placed finish in the SPL.