EncodingUtil.base64Decode() can be used to convert Base64 String to Blob value. Then, the blob value can be used in the Messaging.EmailFileAttachment to attach attachment to the Email. 

Sample Code:

List < Messaging.SingleEmailMessage > listMessages = 
    new List < Messaging.SingleEmailMessage >();
Messaging.SingleEmailMessage objMessage = 
    new Messaging.SingleEmailMessage();
Messaging.EmailFileAttachment objAttachment = 
    new Messaging.EmailFileAttachment();
objAttachment.setContentType( 
    'application/pdf' 
);
objAttachment.setFileName( 
    'Sample.png' 
);
Blob emailBody = EncodingUtil.base64Decode(
    '<Base64 String>'
);
objAttachment.Body = emailBody;
objMessage.setToAddresses( 
    new String[] { '<Email Address>' } 
);
objMessage.setSubject( 'Image Attachment' );
objMessage.setHtmlBody( 
    'Please check the attached Image' 
);
objMessage.setFileAttachments(
    new Messaging.EmailFileAttachment[] { 
        objAttachment 
    } 
); 
listMessages.add( 
    objMessage 
); 
Messaging.sendEmail( 
    listMessages 
);