Michael Stirling was charged after the 28-year-old’s body was found in a rural area near Caverswall, Staffordshire, on Saturday – eight days after her disappearance.
Ms Eastwood had last been seen in uniform leaving work at Royal Stoke Hospital at 7.45am on Friday July 27.
The 32-year-old defendant, who is the brother-in-law of Ms Eastwood’s ex-fiance John Peake, was not required to enter any pleas during a three-minute hearing at North Staffordshire Magistrates’ Court on Monday.
Stirling, wearing a grey sweatshirt, was flanked by two dock officers as he spoke only to confirm his name, address and date of birth.
Staffordshire Police said two other men, aged 28 and 60, who were arrested on suspicion of assisting an offender have been released on conditional bail while inquiries continue.
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The charge states that Stirling allegedly murdered Ms Eastwood between July 26 and August 5 at Baddeley Green.
No members of Ms Eastwood’s family were present at the short hearing.
In a statement released by Staffordshire Police, Ms Eastwood’s family thanked supporters for their efforts.
They said: ‘The family of Samantha would like to ask that their privacy is respected at this terrible time.
‘We would like to say ‘thank you’ to all the people who followed Samantha’s story and tried their best to help.’
Stirling, of Gratton Road, Bucknall, Stoke-on-Trent, was remanded into custody to appear at Stafford Crown Court via live video link on August 8.
More than an hour after the hearing he was led on to a waiting prison van at the back of court, escorted by two security officers, before being driven away.
At Ms Eastwood’s home, a forensics officer was seen going into the semi-detached house carrying white coveralls, and evidence bags.
Outside, floral tributes, including sun flowers, had been left at the front door by neighbours and members of the public touched by her death, and in the front garden, the results of some recent landscaping works which had been carried out.